Best Known (51−36, 51, s)-Nets in Base 4
(51−36, 51, 33)-Net over F4 — Constructive and digital
Digital (15, 51, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
(51−36, 51, 35)-Net over F4 — Digital
Digital (15, 51, 35)-net over F4, using
- net from sequence [i] based on digital (15, 34)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 35, using
(51−36, 51, 105)-Net in Base 4 — Upper bound on s
There is no (15, 51, 106)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(451, 106, S4, 36), but
- the linear programming bound shows that M ≥ 907 219566 160403 704176 293457 515345 858757 089100 371311 122924 007477 969239 010740 634294 714518 600898 650465 367549 566074 081142 476796 395616 774460 995822 115648 959163 888828 416000 / 164 002267 906727 598613 394180 622318 732656 773613 528418 250949 503534 714648 038756 170225 614544 147525 285770 591818 518775 007954 617780 725292 498883 > 451 [i]