Best Known (235, ∞, s)-Nets in Base 3
(235, ∞, 112)-Net over F3 — Constructive and digital
Digital (235, m, 112)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (235, 111)-sequence over F3, using
- t-expansion [i] based on digital (189, 111)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on function field F4/F3 with g(F4) = 79, N(F4) ≥ 2, and N(F4) + N2(F4) ≥ 112 from GarcÃa–Stichtenoth tower as constant field extension [i]
- t-expansion [i] based on digital (189, 111)-sequence over F3, using
(235, ∞, 163)-Net over F3 — Digital
Digital (235, m, 163)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (235, 162)-sequence over F3, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 151 and N(F) ≥ 163, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
(235, ∞, 485)-Net in Base 3 — Upper bound on s
There is no (235, m, 486)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (235, 2908, 486)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32908, 486, S3, 6, 2673), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 64336 511386 724757 439696 320969 667183 346158 530883 009482 400238 493280 574451 436250 225941 264478 447419 723773 510937 277281 464700 024746 777404 027680 803677 060642 388326 351052 479310 640853 447474 794328 904232 071166 889537 561627 504901 107571 088196 271037 660989 835800 510729 919811 043610 587799 228803 206859 871411 322084 605217 819521 193853 396082 630292 104218 618802 248517 056269 583988 017914 743561 838067 009643 551867 776575 123169 716753 582392 889213 223547 564532 292662 494551 916415 784422 197860 503043 541349 609618 883406 819717 155265 286721 429099 852374 602858 934454 637670 834751 467964 022430 304522 780200 545345 049120 535972 650446 260944 486710 429874 541022 481529 742278 469020 356981 321647 909253 811458 143901 875586 580585 573497 118903 173272 480387 549886 102164 455755 355657 525563 123381 480703 972758 877462 028809 169069 024215 552582 415385 087535 844422 623637 126098 077772 557502 033364 346153 109392 487742 838078 619746 033566 749972 538094 182824 274702 612104 723395 278034 372591 117115 939330 920436 168864 802968 580222 743885 196344 150225 394772 053577 891765 767751 504472 032110 022656 352365 554514 535340 380488 353593 341198 285241 522381 660597 965279 851466 567433 337866 805611 431282 448793 250981 540720 325233 878713 680655 938260 007603 474815 950524 871674 778223 584665 538989 874269 291360 948116 292179 678360 442040 716603 886089 844478 604775 965466 552795 400566 662453 862742 150845 378149 904829 788233 801702 675364 431973 348046 352586 829646 178608 638025 515606 711407 043008 324584 587649 348102 237864 458552 703317 514907 / 1337 > 32908 [i]
- extracting embedded OOA [i] would yield OOA(32908, 486, S3, 6, 2673), but