Best Known (31, 31+∞, s)-Nets in Base 128
(31, 31+∞, 288)-Net over F128 — Constructive and digital
Digital (31, m, 288)-net over F128 for arbitrarily large m, using
- net from sequence [i] based on digital (31, 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
(31, 31+∞, 609)-Net over F128 — Digital
Digital (31, m, 609)-net over F128 for arbitrarily large m, using
- net from sequence [i] based on digital (31, 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
(31, 31+∞, 4128)-Net in Base 128 — Upper bound on s
There is no (31, m, 4129)-net in base 128 for arbitrarily large m, because
- m-reduction [i] would yield (31, 4127, 4129)-net in base 128, but
- extracting embedded OOA [i] would yield OA(1284127, 4129, S128, 4096), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 205781 583204 250469 539307 371938 209329 815500 398358 958448 032009 423946 755971 537744 363684 693055 006616 329530 550785 624705 523675 621875 483047 326201 461664 645341 736337 597627 179936 754314 508156 482385 341146 855544 164113 011927 191151 072316 379602 593981 383145 639456 145918 907586 917062 244128 702009 078048 731234 886016 174080 763803 098341 046146 316918 500225 546141 242899 421684 172161 967354 713249 269959 365428 502899 319420 873773 663045 437095 201149 130897 322942 525329 074748 503497 730347 993193 148179 882286 456254 753063 831828 821460 100908 541015 338689 880613 437635 873209 589544 421671 492839 815424 274291 605589 225166 699479 248192 567573 609705 302526 832070 194912 952647 443371 324319 085835 677209 478749 642007 720914 976675 185719 364814 467692 799809 319575 230462 524125 338264 376008 642606 814691 460833 699789 720024 566972 243652 696024 546225 416280 553133 111284 030612 419378 060288 161379 374981 634756 738793 116047 102196 275856 488769 648065 687770 507575 024409 770691 957613 351675 148470 930556 905191 809585 575236 370695 452909 773762 095855 483892 185285 858109 888899 748194 392388 612207 028923 023402 971879 529193 016684 282745 600958 298552 886306 940201 198111 245674 325362 637898 354616 012370 816956 612459 267827 878329 142599 896618 673274 892061 700151 284837 006795 627848 910485 096958 407822 227021 244520 475169 250653 137707 953431 196225 280188 285211 301825 516808 221799 491476 478594 622764 628231 576325 293832 669908 147530 446542 207505 501178 915975 161699 996180 564257 584442 719240 770902 942452 117120 942898 391239 750702 741569 168972 566682 011091 718373 579659 223482 688657 151538 066634 718575 972906 221559 616711 206445 082452 219701 964370 265627 200747 142826 292453 776723 371817 753499 584790 520387 476907 120771 546635 877293 310693 323560 877446 055822 373553 862719 226918 013989 437514 738734 004169 791430 380448 926921 482158 590858 156797 941213 228952 181904 948028 702597 494161 712718 545159 836646 069010 322333 597680 846556 177911 921037 292404 457119 841529 674697 722546 981758 776522 706850 943839 431566 381056 658929 837123 198926 575038 080063 592588 573651 905444 070623 127905 914302 966152 589868 711678 372594 170403 280079 645491 051328 950537 227355 290940 178018 703991 853636 907071 442160 783787 967250 881772 044817 947673 062506 556913 924836 172351 273113 447169 569993 592264 244078 257378 722132 709263 270064 942216 667909 978650 000445 501439 903607 992150 224267 748101 573082 250170 271677 613910 521991 244439 266400 829249 513134 610288 027441 431377 227398 162997 082441 385396 117721 002325 061781 788812 943887 051740 463739 702461 753694 590102 537277 514853 500985 540286 137181 743187 175334 348832 838400 591252 230160 385198 073822 557923 011225 161766 693687 914688 179705 089844 457975 105061 334783 835811 412255 200939 162420 309941 309746 084708 845451 250759 187099 371160 094688 034767 840427 449458 511505 282843 217210 968364 768159 605495 794915 291285 110354 135421 351248 347531 877321 010300 076222 567670 341809 841151 750795 424466 651666 082013 824920 299024 031167 206229 584866 080754 489032 536659 291578 470569 125299 039734 334225 027313 868901 754035 231878 765363 766643 925146 131480 191142 198620 969363 109512 810845 904268 518312 891319 265429 628559 421221 074276 573737 455171 694504 381475 830050 064027 254460 690483 891136 991764 157909 600931 377517 436569 095369 384828 761129 371904 003919 302906 528007 089015 983132 157958 360195 632946 444462 811807 798983 049542 800345 301832 075640 872222 138620 785041 781935 605716 283232 267261 475601 453911 465847 399626 624714 320428 008202 510561 528458 011280 237970 673064 337632 688195 649071 081878 205957 967090 856963 839579 929108 676127 460167 154573 764783 845163 026905 845874 801223 336092 973783 981584 639015 631481 561742 981640 537518 292953 525037 452647 241015 075443 878969 355631 511401 774421 951131 012117 966251 143620 957502 353793 054053 965987 420521 972123 305558 999987 347794 260945 721791 384854 906647 901656 590169 173859 024994 207484 049592 158808 043049 393697 683974 876396 830975 201503 729970 566491 208171 457094 322809 032265 575899 180877 740782 585016 797992 722688 929091 815280 439453 620537 196466 418352 875865 601589 945591 374853 313935 176938 088496 654220 393084 456602 425533 622608 269319 607564 502356 106928 508557 235923 433230 677284 723803 657622 277970 673433 870054 826787 359738 924096 087823 877925 658150 746830 670055 768004 517400 795720 494056 102517 951948 590935 915619 348271 668904 798331 728447 739041 220192 148993 329614 861278 318073 757731 866956 770547 044082 038797 987051 545196 326795 370264 622785 234931 795920 792204 886259 601777 458153 406171 698354 102106 451374 895932 606237 680921 776319 431387 954613 051922 327354 169536 938724 135181 101391 083320 428447 017014 254687 296492 337372 816807 401083 816626 712918 444380 683775 286420 105256 551213 805553 248313 809697 015718 296479 286208 251775 631671 380723 160298 582712 125100 606881 561697 453998 926435 405995 225954 303774 826745 144282 186349 203724 852211 745288 196143 994202 811070 021186 923868 426372 782456 154356 448772 761265 539458 262063 744411 413137 440443 990600 698417 798990 592642 748424 884906 208775 096339 350655 668016 402789 183283 999273 224304 836952 175379 922500 722631 664932 248249 690557 470378 246690 713106 787852 827026 910022 912790 143019 621490 577619 189058 107582 927317 272266 526171 670690 230728 881409 950203 891942 225942 017317 902168 352307 896222 277515 545034 319325 739450 192792 988773 881126 893714 082070 964413 126565 419076 570583 867965 763315 557345 970096 358990 720150 128802 505300 925052 182392 979830 576401 418479 092839 244491 193139 736611 032836 110230 912912 424585 897957 193155 769928 213160 698001 004880 309831 543377 490240 681850 013594 415963 066741 243251 201141 436189 285304 183243 982533 839469 389476 456060 448117 382166 389270 613612 925677 628839 426316 280307 394232 302459 673804 387739 441475 731299 396863 803491 342215 485467 765544 567049 624339 301528 467925 010439 750632 139304 684565 249036 062241 763830 731765 614701 411600 364235 236573 399819 965188 518200 469635 211750 070826 532592 132788 285005 016505 842045 105544 763826 898836 512585 271098 796469 899728 657518 326796 561937 956320 688067 960709 422442 953793 336248 776252 493249 870351 325830 148529 918628 316529 954922 610768 308173 283265 527740 573981 305078 114323 248692 388945 058794 402122 013202 683621 778038 814001 250507 511457 038708 574715 054109 858183 751357 985236 847225 077724 839759 020842 771801 383635 894657 878353 478805 859553 925384 428447 132160 544660 270716 389440 320119 623794 113824 874911 274056 169835 255876 896663 642400 317624 643874 017056 210401 665371 636567 538068 008178 447278 353891 149953 513173 000050 753349 313603 649817 111669 581924 398834 460053 181369 386448 796140 791656 541063 900429 836966 150553 306504 654501 924321 293632 074930 879077 489072 417066 002897 477345 449657 632907 438494 732142 001017 819775 661127 037829 805139 727390 713301 223501 486732 190490 877750 032268 724316 402784 755289 675555 986289 708101 206449 973101 329970 944010 837247 042418 713507 150551 428685 777954 198857 771801 163231 342110 635401 956898 586308 012487 710225 211749 436666 516657 980157 103185 977047 602192 606324 387484 883027 248054 300750 646266 047593 358881 150914 805933 115196 979000 607513 898186 727305 050175 308125 987022 957791 745186 999994 886611 494345 477826 923396 083730 281312 527493 539148 630729 862843 371445 072421 605777 395930 917156 237495 370287 362291 224251 777029 146086 984440 729840 951662 912082 570931 894692 553031 051349 968194 215697 471917 148833 395758 548334 406434 166648 422775 196897 490810 794776 462395 695530 471252 200164 366599 507826 816503 641817 482450 099446 054084 379207 143303 283946 486669 457957 527650 714313 840390 639129 985811 977751 031973 269042 529500 957497 397024 448504 570913 761246 472298 820651 683415 197284 902630 583996 101722 975208 213735 510314 572671 966923 223471 221998 726339 840633 168610 241918 925980 553531 665945 590554 454043 921389 854888 679689 204090 925523 079076 410466 518233 974948 753829 675154 354318 354595 941259 142576 467962 940169 231863 490845 222218 538389 766429 661996 690064 291908 516654 338918 927990 369072 624002 435054 604736 116664 529564 269444 860353 471902 383810 552068 869315 587449 819513 836607 827346 012150 266621 696269 833707 557365 640848 660569 029368 926971 613198 160974 587203 181571 388075 248323 229787 548517 857351 688415 550163 176847 858497 848495 769750 598339 578928 422653 308175 199166 475493 316031 957997 473324 872374 756254 536068 366251 297340 000300 674510 863835 814899 482616 416209 453175 540046 763981 176249 196474 364508 234921 003408 497868 638550 849104 924606 174344 151227 231191 590987 929195 374739 518429 319539 855629 038981 052694 671950 342598 911306 175231 850206 278191 409017 571606 008992 057562 766095 018478 973352 230758 810151 637840 595998 186000 981210 892442 824982 001000 381274 739309 226313 952199 537064 135546 126272 810901 493195 821218 754965 846045 371272 723171 368911 390598 600542 953699 959659 280938 643696 729106 424312 010864 086239 522822 552344 983100 133657 839504 545897 271164 730647 153593 307336 826496 984843 937517 295460 551227 065528 244282 079642 266053 037925 528959 512113 242154 515841 304136 112631 129341 058991 916373 243874 649110 998526 168165 123940 261651 071390 055734 154076 383200 610929 696687 543266 971502 254969 439752 819011 359551 155151 854470 080728 879667 712460 255209 834302 071229 518878 880789 322527 836634 556287 443180 584438 804792 747052 873964 188304 471813 167044 149094 983112 928882 873974 917682 626384 968849 202642 493633 922147 239581 993201 224080 639167 416126 657134 489676 910223 181512 892130 559423 754618 224737 289703 313465 027648 002900 296890 028820 875366 090870 576278 703780 816918 193393 999318 725720 321172 238818 279857 998141 777736 664601 202558 490921 854802 742146 141125 623971 202236 212039 385088 / 4097 > 1284127 [i]
- extracting embedded OOA [i] would yield OA(1284127, 4129, S128, 4096), but