Best Known (76−46, 76, s)-Nets in Base 3
(76−46, 76, 37)-Net over F3 — Constructive and digital
Digital (30, 76, 37)-net over F3, using
- t-expansion [i] based on digital (27, 76, 37)-net over F3, using
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 26, N(F) = 36, and 1 place with degree 2 [i] based on function field F/F3 with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
(76−46, 76, 42)-Net over F3 — Digital
Digital (30, 76, 42)-net over F3, using
- t-expansion [i] based on digital (29, 76, 42)-net over F3, using
- net from sequence [i] based on digital (29, 41)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 29 and N(F) ≥ 42, using
- net from sequence [i] based on digital (29, 41)-sequence over F3, using
(76−46, 76, 140)-Net in Base 3 — Upper bound on s
There is no (30, 76, 141)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(376, 141, S3, 46), but
- the linear programming bound shows that M ≥ 1239 425902 701167 359387 634027 779408 519762 709262 383373 969093 013055 394189 451321 855434 419134 955995 578843 428108 571632 231710 187419 868518 256583 326241 168944 252882 398735 979398 922721 553289 167661 439278 006937 289846 459956 997182 334962 086820 293756 300752 234920 627744 965167 159378 951150 671742 092706 567678 330701 / 619 151021 745863 958229 474937 131529 581480 994844 744514 155471 198189 416920 526044 642490 200443 004626 495589 553207 277337 934597 756407 331144 456306 914384 534916 851146 560682 812459 331622 620796 601820 969552 710112 741666 982370 750873 449648 332022 999009 114022 310456 252406 916425 > 376 [i]