Best Known (35, ∞, s)-Nets in Base 128
(35, ∞, 288)-Net over F128 — Constructive and digital
Digital (35, m, 288)-net over F128 for arbitrarily large m, using
- net from sequence [i] based on digital (35, 287)-sequence over F128, using
- t-expansion [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- t-expansion [i] based on digital (9, 287)-sequence over F128, using
(35, ∞, 609)-Net over F128 — Digital
Digital (35, m, 609)-net over F128 for arbitrarily large m, using
- net from sequence [i] based on digital (35, 608)-sequence over F128, using
- t-expansion [i] based on digital (30, 608)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 30 and N(F) ≥ 609, using
- t-expansion [i] based on digital (30, 608)-sequence over F128, using
(35, ∞, 4644)-Net in Base 128 — Upper bound on s
There is no (35, m, 4645)-net in base 128 for arbitrarily large m, because
- m-reduction [i] would yield (35, 4643, 4645)-net in base 128, but
- extracting embedded OOA [i] would yield OA(1284643, 4645, S128, 4608), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 28 268370 109316 500062 432625 767146 206200 066366 347887 451091 044476 912929 501718 283647 139555 850865 962377 998412 054477 461981 012437 897750 789914 749476 951397 075141 273079 640582 509050 897304 814845 542079 376186 736636 139535 064209 698196 774290 589898 185747 713227 255383 596871 835628 514343 615042 807551 623274 605332 581092 645952 563773 974517 532857 994371 081322 660057 395837 690879 046275 279036 271077 509288 428536 622782 876026 828342 854096 508810 475823 304242 143365 936045 048327 169263 023680 101814 633760 757722 772672 264121 112940 017195 549740 759123 781930 821269 436075 527175 234336 529654 513709 088638 898364 765138 924684 594938 154060 052542 261229 956165 968006 375383 024048 636288 856698 934813 460089 098742 053348 307072 454251 238709 248362 862588 607607 799242 995927 435404 690639 973658 672217 548657 814657 077663 625811 864419 867660 254157 112499 772737 190564 278774 795157 405942 040508 263110 712711 815494 212437 831087 739865 012780 671708 620995 895913 096009 453764 484546 773333 829226 499460 173094 933417 808294 712656 653393 088276 973058 496739 286170 789893 415226 616313 292762 971616 488954 426965 166608 481552 694608 227437 962808 944810 979491 739020 980911 874178 589324 194098 968760 939606 994625 207801 749883 543258 566058 938815 572048 889850 431909 526829 678364 618679 236299 400823 728782 028971 858284 182012 197249 642697 207527 193950 190430 681890 144951 494313 119773 715162 473795 203049 111482 674905 391403 718233 625408 472755 718848 357272 434493 849203 991642 542679 368640 558902 433769 811882 078545 840446 904421 317440 783586 969503 449433 491687 059202 601177 336124 981849 785789 599170 386010 794158 064524 405815 733166 974629 810904 765646 178662 735727 592518 763853 671718 508322 028837 300693 939041 245737 970610 760011 124868 092129 019530 536303 361160 673611 832548 270375 722414 986770 003708 190213 212646 891406 060107 347715 784013 762588 059356 574069 635990 452174 754493 985938 231794 790773 773258 832714 731763 561215 328120 702727 887360 760997 783034 942387 126953 176500 459600 303195 378245 400084 834269 690701 272261 142208 206699 586599 945868 881140 938158 479335 630097 292030 979080 799716 672303 201928 053777 159107 342202 074759 443000 053525 590357 127919 164366 409198 347793 939966 335129 716096 252759 256654 462813 341721 022741 286290 554224 029704 707104 035039 180893 994542 296069 265313 774117 238309 189293 854442 729245 173897 516507 124003 513298 020273 747763 083669 425219 695757 837996 521549 551541 574189 327742 899985 105247 843942 921006 861819 836744 030277 081299 672906 236329 697873 025186 617619 933160 284114 829962 343981 975478 769696 613477 680583 699780 884190 862423 528538 825248 452575 675748 832785 647017 507116 527540 305615 722327 927740 771719 380866 058613 184159 504715 762344 463481 814740 248019 871948 921524 781154 010275 520369 839938 270032 044624 793942 112928 688832 073899 389237 608594 509318 579160 622871 108893 123568 032344 328478 587626 518059 842259 586508 949548 988533 967617 753714 081379 725658 401540 619568 952922 181763 380110 324066 107078 052831 833234 084918 988868 215218 316981 187140 458599 121120 262205 767941 762676 555358 777198 620884 203080 830966 046027 642717 247123 117364 795002 150012 869090 670557 964233 006717 805119 689068 170775 377168 142251 112489 979367 003687 571788 920183 131112 705189 139254 773401 580753 166560 140245 227232 819257 094932 871928 072883 976552 660745 896283 210511 158461 627405 571246 255045 268705 826615 086006 998257 128069 561894 596359 710366 247457 736106 386468 022308 130519 424980 931768 894625 773838 950062 372066 871602 319234 345931 780462 807415 036186 146198 932080 243970 638540 699734 553845 427419 998230 551230 273579 950384 024858 860430 772625 093465 196292 543695 303710 395702 340958 226204 440163 496138 172976 801465 603444 462975 430853 735445 561435 747653 433358 963088 526178 347638 234843 491533 737136 208790 277483 279458 373218 385177 929477 423148 886495 906443 365293 280799 535257 158982 200303 500268 251159 527402 963065 867259 241999 892385 036371 053353 105625 283642 885256 528437 966385 230504 295774 431985 532423 588287 183571 683454 298220 099478 016340 412691 954696 181779 275100 798677 884286 195583 347301 818768 932059 134808 138920 979421 689972 608861 346762 670021 242738 112955 326799 939979 570771 187724 114812 076071 432533 784685 395590 700884 517328 588979 488623 049361 620664 488896 216202 347345 458624 120843 850450 662193 712052 090673 372540 111667 410455 975464 853488 956833 904820 189782 080993 778150 970559 502433 100531 743314 212967 909758 417461 266754 734310 909817 406423 835050 897588 305039 030704 055811 621471 470957 229160 617895 991965 660195 605405 407990 075882 908327 691021 040459 474190 129995 215460 884826 747446 743807 499552 344446 485521 109782 554256 041999 033085 325774 928882 602751 473668 093295 752285 902214 700013 748772 750597 548971 713345 986880 730895 467646 904265 872851 371652 905536 961378 561939 969794 075072 893710 196147 685524 633028 915780 693298 159496 385256 053948 687298 668872 456042 051218 507068 792862 778422 413055 919617 131446 058306 617712 688814 269373 966393 157998 880282 404927 302457 384762 175678 073949 684034 488523 768024 038833 307392 048368 278066 461427 412160 770821 825862 828712 890365 680056 396725 503978 673420 712965 705794 335616 724786 995212 870104 528055 646543 732306 633609 385707 526342 175493 463444 998644 973638 348751 497394 089394 845340 607375 202377 838933 056325 661378 872250 179936 040027 215701 853507 373249 017772 524850 928342 054904 237606 559504 132246 613518 970478 706977 334012 317703 832347 307464 820203 100906 636590 890396 931651 667840 395151 436586 558805 324738 941112 893886 618162 911917 350120 850723 888387 049806 753389 914070 207077 954804 135284 960033 215116 085454 349259 962722 686779 441291 037246 037821 073674 760246 942833 733465 198965 517022 257496 725373 970091 711940 644685 249418 702115 222103 822987 564431 580225 891921 307718 759280 627604 206118 037688 359549 894025 773399 771336 721354 983379 876923 049245 626805 611904 003218 503722 646448 401961 401447 869995 967076 971167 605474 680851 460075 681820 089333 014081 286837 262112 252164 768884 867834 118199 683551 964442 653226 205835 209741 669963 226063 848232 710445 626560 009675 498249 603800 032797 970778 054446 916152 847443 894079 190736 205429 055236 152304 382926 239831 633015 550933 978483 057304 241135 464921 290769 471443 077937 626074 345400 975348 038881 236018 948216 711507 527996 704628 016618 970387 888974 482171 983110 904364 857494 763531 317245 218603 144419 045165 487251 215793 720603 454976 171549 068082 808341 105898 417909 484695 937277 548367 643070 235787 506863 115455 566291 773417 541507 474411 612686 506334 843568 768645 482919 600946 502213 620080 328664 713867 579683 367704 221068 228472 303517 430132 137496 250578 345614 216522 671662 125379 199838 761608 579012 600387 409681 958046 927378 344274 538245 844009 910852 559192 086942 120528 470373 107147 131474 274642 045102 047110 200310 277117 669920 478983 858376 633364 392451 849244 917671 207946 286002 391104 409574 503650 524463 876681 205979 879644 165091 470738 139073 544492 259960 942806 795877 093485 049650 111797 533598 710444 773735 738199 381290 680946 515940 293883 605586 749012 059947 005068 309875 454489 007836 785953 918887 911643 272087 017141 759038 573951 186502 721825 341398 621303 630434 269903 680073 036748 535705 305374 742985 955081 958418 712555 597614 856487 564769 019352 739888 544607 195982 758876 933091 929602 678356 998072 968632 232449 919621 114135 946767 018748 472145 506259 805699 698148 082468 423274 768486 437472 048654 811756 490998 769157 600740 768675 897973 923768 763777 977707 982111 700185 831490 694636 009051 598735 413984 119932 912134 927877 679406 961244 471148 423870 981008 368999 092669 961002 965644 219058 756721 281230 667475 166052 690156 775566 543291 923585 134797 403728 797463 493782 705890 979279 691697 800900 451566 245915 718575 218940 252979 586485 284766 156167 596265 036847 803872 099040 073593 522098 957500 195602 322612 903382 606170 132216 404158 408230 013537 204994 313038 664542 375891 333612 794628 322560 049687 256296 372913 485039 797008 196024 187994 597131 489136 917221 776730 028518 681154 836872 668027 817144 811485 821438 336593 883303 572177 074944 870580 374987 256454 286792 437005 600270 091106 135460 139150 453032 036410 183573 533287 582459 810914 705054 367648 449192 718882 535887 122101 229260 021682 524022 828765 926968 006254 667368 368021 570179 990073 454554 403027 805674 748194 976943 728892 092893 209208 928760 763812 558867 628945 182044 589520 242037 888115 959384 378917 069534 148435 773169 106487 673518 251014 172614 388600 242018 113030 679792 065159 044919 887148 285906 439226 549642 076976 704890 018657 361760 970760 516016 808746 830951 735249 114386 689958 091013 196357 865655 310533 938441 979689 780342 350938 967397 131051 930234 931274 836832 141121 273221 326432 093883 186364 702507 596701 299522 170272 175509 220349 530472 540448 368764 270853 254775 479069 977686 686758 910064 933110 612976 563518 953872 282068 877817 904490 644098 399769 144430 069921 713283 596825 941420 998081 440130 045043 296484 747711 238319 421458 497291 015990 776745 653628 613937 699268 354062 578486 689268 924552 344887 006035 763309 879930 743964 114953 150844 057959 840271 756886 409595 462729 262083 899149 463578 578153 253023 598127 175775 761527 820818 838890 171750 371168 205144 308552 194658 159332 086494 851242 325164 312958 112397 912945 318954 340266 915736 397765 133557 435993 469046 782147 461883 066756 835002 921761 525568 621677 109155 197788 844537 609150 593506 766460 164850 753956 298006 394987 801635 045587 317613 033210 646258 592213 878256 085424 249499 324583 491076 420376 875977 387005 293759 685473 125409 214554 898370 104546 373751 432466 535348 673973 330830 851103 435096 916333 058645 786416 720939 033532 880796 150599 179141 236491 080038 595998 559484 013439 543627 091534 410563 120050 549209 520517 191894 839404 052903 308389 596641 667480 825707 716853 187422 315711 420820 023234 655089 713663 223781 079090 024334 651034 742874 970806 881806 294112 201423 379964 706800 862595 271739 137501 748932 903898 860122 663077 285404 343269 255132 582785 060343 109313 883572 076776 871489 470958 163864 916501 215939 573705 140071 912384 554909 711538 139324 118108 808180 586886 479595 810635 600882 992050 563870 773159 917751 093298 922025 432598 983158 109124 884767 695102 307076 348993 978832 190894 527413 578316 096526 162767 815489 407626 942412 949643 699510 836650 836522 495949 194420 842164 121430 013877 580368 474801 179934 296939 466460 408448 714026 773148 936880 144292 959623 112016 022430 431736 290015 659820 327737 826091 734516 654191 342434 720729 605961 966794 039890 621633 854332 012020 405886 042837 531494 765523 513754 600482 973499 024489 489507 840574 589906 052813 382282 892542 794886 407322 628385 921504 034854 740321 411532 059242 163406 620425 275767 141215 345849 657042 273744 344530 455667 095125 631934 160623 307268 697360 105391 710057 973692 712500 079081 302934 664334 377136 853161 116121 863720 589107 021559 937733 202851 447472 440235 828250 304082 890647 644143 398504 995290 224168 999122 733317 370226 409472 / 4609 > 1284643 [i]
- extracting embedded OOA [i] would yield OA(1284643, 4645, S128, 4608), but