Best Known (75−45, 75, s)-Nets in Base 3
(75−45, 75, 37)-Net over F3 — Constructive and digital
Digital (30, 75, 37)-net over F3, using
- t-expansion [i] based on digital (27, 75, 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
(75−45, 75, 42)-Net over F3 — Digital
Digital (30, 75, 42)-net over F3, using
- t-expansion [i] based on digital (29, 75, 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
(75−45, 75, 147)-Net in Base 3 — Upper bound on s
There is no (30, 75, 148)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(375, 148, S3, 45), but
- the linear programming bound shows that M ≥ 590 120846 623377 656391 069611 419462 478892 700111 332235 753542 892978 964081 186500 581837 397525 439282 627472 097286 950369 041256 226115 254166 206219 748203 859328 746017 067633 491684 819772 271401 346832 059505 067379 993239 767275 842410 377928 173211 258457 224366 465382 215796 051686 653704 753388 169641 277219 669316 425315 179848 202413 868104 710118 413044 518919 058715 102177 180355 338024 292294 755043 575759 / 875 283163 572176 128193 747686 199754 076313 595617 360350 823278 793844 480930 816971 707313 086974 061443 650139 220826 606324 078439 870380 390239 549832 592829 508396 019427 758043 098233 935504 073091 399672 564689 457449 221176 207597 355744 849697 870861 217835 478980 011951 210294 662331 675715 140506 357595 012793 982579 054478 875395 189571 057565 271813 852959 656730 623375 > 375 [i]