Best Known (107, 107+∞, s)-Nets in Base 27
(107, 107+∞, 324)-Net over F27 — Constructive and digital
Digital (107, m, 324)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (107, 323)-sequence over F27, using
- t-expansion [i] based on digital (72, 323)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
- F4 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
- t-expansion [i] based on digital (72, 323)-sequence over F27, using
(107, 107+∞, 325)-Net over F27 — Digital
Digital (107, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (107, 324)-sequence over F27, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 48 and N(F) ≥ 325, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
(107, 107+∞, 2845)-Net in Base 27 — Upper bound on s
There is no (107, m, 2846)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (107, 5689, 2846)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(275689, 2846, S27, 2, 5582), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 21813 365035 049914 274004 306938 870822 579781 129132 996631 861874 879224 265225 511077 018016 396394 580774 078184 455385 802034 957329 313758 689721 537601 025316 816182 338055 068287 893573 885140 239146 592971 267257 473941 487881 809759 596670 374675 155250 408154 950977 206885 115907 813308 716400 021239 830176 868817 212776 511931 202743 337019 061011 582683 172570 086197 941250 610057 021985 007191 298372 914237 329749 621620 159416 184786 217007 911348 336204 783711 513100 916815 841738 919609 558947 477987 262953 146035 533107 366226 124104 063131 374099 418164 546872 019460 517184 116296 679181 207440 233012 420288 572586 781587 301764 741336 879172 459703 359578 817902 439851 326935 156915 941093 249691 699336 574830 079527 595986 919929 696668 687577 175272 890479 650922 965767 862334 911270 652572 203593 654806 782977 768481 793016 792212 489583 857526 372344 916517 182064 116582 354120 179481 163947 732604 398512 102190 118117 008405 661924 060002 350524 296322 960805 549165 790652 968516 828618 112404 281659 541401 394516 059875 292036 807261 979233 498325 375225 935364 794645 713438 695847 650248 335888 069622 686323 149635 520551 819730 645957 040717 684044 357796 585482 525875 696573 165351 940811 865761 390458 381357 828223 547315 593498 030701 347442 590747 515098 987628 679647 834787 528541 637694 391590 674137 452433 188349 351890 490900 367983 445660 217424 635193 393723 638735 728180 255237 838361 577966 620580 982288 748423 624711 264408 146195 527062 762792 184000 849308 230913 108875 385013 698341 880525 848629 523588 208654 872975 761160 220409 977948 823191 299541 537654 720218 212304 486136 103687 677770 598952 948371 162647 003535 570546 853427 548779 199620 986922 935283 055034 831217 117946 077370 533586 420492 416152 467967 033211 561740 433106 456361 072924 250514 850527 239840 480429 787520 163898 631590 056521 486768 297905 025749 144630 242140 777050 298890 480107 170378 306061 113636 332505 455776 000522 544615 384918 149387 319589 402800 735522 640969 638751 770247 415180 302306 612977 318152 516810 682244 824964 640306 275374 499011 845466 390703 066807 598861 096290 497715 256201 941958 719933 483918 232126 394622 585384 433478 656397 273888 477978 114443 617378 145132 499135 436210 990408 293825 014829 213127 507847 663621 821857 893006 681452 438954 357047 182484 811684 101117 586125 315806 982932 352109 956036 936906 168106 649314 095931 931187 829055 608841 856479 446074 359381 036083 885523 961082 731308 245219 459757 907192 162423 186614 771146 311974 963334 866216 262143 308816 841328 625580 478585 897355 152532 615512 980408 160920 790883 673961 260910 428264 771359 315086 170939 986710 590323 272750 952573 921342 106243 978758 467812 146629 775212 931074 591832 086709 796120 617293 522959 048107 249827 949909 258910 369008 176743 221981 010171 683804 043357 948149 605103 758668 075623 285991 875305 185492 891112 373999 003196 507819 168257 804305 403116 173923 270956 659172 680187 654621 316204 605438 969316 872009 143596 850167 574810 767692 837294 757114 137678 340920 011120 592972 293035 662408 740707 768223 064180 379386 456657 796638 807579 699224 246321 242933 319520 578431 879556 825580 997807 439999 440662 824012 613379 132505 606209 596226 835337 995778 997820 542544 326373 276520 133744 369524 611641 205111 711146 994696 756264 267574 150111 283432 161356 026422 281989 941660 499771 879250 610565 257838 625728 766417 308812 110354 671635 680961 432768 705246 289308 738902 460329 259122 018504 430980 834656 740694 263568 197020 597972 406631 949304 696810 155895 859540 561652 485629 984333 392392 345876 473400 138255 933669 609114 507877 716985 327807 747093 294553 295598 702777 170520 510261 623668 341683 275677 909731 131651 211386 869389 702158 132763 728484 425470 040864 645158 798682 691835 494045 019458 448802 157576 346929 987083 084038 601365 247884 457668 238593 895191 246515 795135 485978 758745 731257 896787 946615 790158 252259 879857 486342 727106 286274 961267 843291 469038 065189 320157 570079 816951 568861 908617 061416 959759 656874 502239 876728 984747 673941 079766 818664 811917 486414 245573 481160 217449 118392 160246 077708 203025 124527 021550 506887 819421 534939 981584 065884 354924 577921 128129 541688 158403 170066 886085 785397 203039 877527 496341 048611 948255 208478 509226 201794 647339 339019 942653 263939 923052 256557 083374 165285 064178 280034 339039 960425 707611 686649 123483 560202 766910 588738 716764 340085 712564 728572 597334 686035 558737 710393 147106 687063 351698 197985 441424 678169 336729 907335 871638 161775 732285 567115 802851 585052 446284 259553 104330 410464 751359 152738 351040 885041 466304 091142 881985 806616 041089 287853 367846 012028 490110 899135 670856 179401 879563 801471 584166 384745 427381 671435 198454 089386 913540 686439 381114 305428 306953 581722 235454 205765 760657 299237 901414 855561 516357 256179 022283 973814 094689 331356 587080 578496 189691 173434 921307 650727 290641 208295 117223 388634 513416 594344 383057 790089 604930 384208 772158 884117 687575 396792 514088 411666 234389 825844 657999 785394 118034 639912 234340 240003 669628 236550 349826 891553 964527 489494 744770 333613 289822 948007 020542 821373 775309 554704 904854 905226 564109 472321 481644 097590 452231 191456 212238 123013 524571 655926 094337 213121 145916 135513 010044 562546 271851 939304 542618 776316 525557 912856 400015 960314 444573 933343 497351 867243 762952 349576 869814 987354 555870 076352 501363 194930 853115 067019 709140 255645 394450 199395 256789 502598 094803 887102 036887 763862 442969 492584 843777 267514 986300 528740 075169 136899 135715 016076 347971 113434 930830 276347 649937 407328 010174 696678 358915 242586 394105 677195 819236 627111 223802 222237 584703 445522 481659 608098 598001 519414 544023 392266 389109 851088 490181 709084 685645 312342 713660 201440 959118 597233 231446 334038 476636 390683 086623 016504 821293 979589 075035 303668 411312 300464 886088 556070 334676 995219 623392 106484 515687 706758 159991 625980 581183 397242 790807 975816 367508 354072 411514 535262 624769 170569 252482 241658 364495 401182 244675 216148 461926 466027 899856 048665 414608 495848 437253 166105 770484 902919 395651 191593 930692 170541 768428 530602 860338 197973 186458 227402 996379 906074 401140 807571 764892 499118 615578 421631 363694 165928 947229 219385 206127 723711 328891 644559 901551 917917 443853 633529 561877 044032 412294 470530 992226 260646 427067 677292 616769 642611 163485 078596 681900 171471 149557 938474 924177 359009 097550 160478 741433 069800 862604 584477 852620 084985 352330 663885 730712 341313 757020 018515 120114 251927 427013 339495 333449 578404 456159 369596 618092 821320 600126 239650 356850 170468 164260 389963 012290 051999 310505 983343 323934 821329 076255 810726 607197 117396 616213 644509 823686 048747 082775 565681 365234 298111 646567 969312 579420 715286 159414 934212 645118 348508 490493 326072 241590 084912 349139 806871 862921 806392 227304 810020 776399 140649 948260 301356 604587 161362 192212 961562 333561 460975 275720 654026 265606 571044 209051 581693 049018 508869 179101 151420 172399 077249 653469 054783 714075 005837 546629 815506 197650 868534 771353 746439 377384 962658 319978 531483 719707 392193 092599 200401 987565 587019 131169 509810 911613 709377 033675 511941 850174 406870 055438 699161 285672 146401 038422 016103 674469 013759 456217 455460 391971 769777 613351 014141 174243 596029 631711 441437 440609 170200 262058 847196 659458 444408 628101 418595 369394 981308 858313 673531 284144 089287 351973 212698 607042 665260 113349 758302 908448 002181 031161 390702 663982 922938 951378 978991 292290 067165 737930 617550 315999 061290 068388 164498 373003 451217 597928 616046 538714 928102 508243 347830 422048 522617 489387 717493 867719 473280 099157 353665 970435 426556 958806 257630 820716 407791 037184 541057 856310 540486 282374 441360 918858 957056 214537 789034 034499 271571 917996 701513 818219 989788 465153 650039 600626 700884 465366 237484 448498 036832 546840 186410 661916 489222 391406 025763 014150 581529 705194 926816 066133 848021 150867 641249 951616 636593 626601 576407 486612 718888 433340 770574 281753 349258 520004 267878 431399 026750 563497 620273 552682 745271 495050 003631 761139 051229 851158 641874 138836 741455 722984 553822 709015 181806 847400 023393 628011 073365 327340 309766 533983 497307 680864 419185 831069 598588 055188 073681 938494 812942 952873 051277 466792 713689 929970 343476 488221 977487 624704 250222 000508 921713 916741 374690 474365 316248 577762 738234 627577 681016 846709 926957 007515 314639 698758 235220 104118 168170 074554 356201 732049 669914 308540 931726 320422 770771 896961 891057 435295 435204 253865 996496 172701 294291 654263 585724 542088 821301 868993 636188 800119 073326 394544 878246 954378 540043 455464 384169 872158 354724 772921 744077 589285 548174 651522 610104 534094 086868 549808 684687 128504 952636 913395 307651 446323 914924 317868 247126 912677 524134 939293 793376 382284 123114 596872 031277 139681 963940 109313 922510 386127 842315 770795 688414 236873 199282 961683 368128 098238 571950 386628 982589 326157 208034 439727 871001 901683 012703 551841 629638 411551 039228 664862 478609 308112 626035 500312 327520 513423 915203 388710 466574 665008 408057 111679 560941 922360 231519 408599 409215 577142 425306 804637 633971 278685 776438 480466 501460 005310 169241 / 1861 > 275689 [i]
- extracting embedded OOA [i] would yield OOA(275689, 2846, S27, 2, 5582), but