Best Known (59−47, 59, s)-Nets in Base 8
(59−47, 59, 48)-Net over F8 — Constructive and digital
Digital (12, 59, 48)-net over F8, using
- t-expansion [i] based on digital (11, 59, 48)-net over F8, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
(59−47, 59, 49)-Net over F8 — Digital
Digital (12, 59, 49)-net over F8, using
- net from sequence [i] based on digital (12, 48)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 12 and N(F) ≥ 49, using
(59−47, 59, 227)-Net in Base 8 — Upper bound on s
There is no (12, 59, 228)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(859, 228, S8, 47), but
- the linear programming bound shows that M ≥ 4 462800 294451 815489 911426 659069 593398 791085 434676 095530 312228 399832 838195 256782 995332 216724 808281 285028 495746 505113 600000 / 21 108871 835759 357143 956443 533552 074383 643233 187346 935658 076259 759713 > 859 [i]