Best Known (71−59, 71, s)-Nets in Base 128
(71−59, 71, 288)-Net over F128 — Constructive and digital
Digital (12, 71, 288)-net over F128, using
- t-expansion [i] based on digital (9, 71, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
(71−59, 71, 321)-Net over F128 — Digital
Digital (12, 71, 321)-net over F128, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 12 and N(F) ≥ 321, using
(71−59, 71, 11197)-Net in Base 128 — Upper bound on s
There is no (12, 71, 11198)-net in base 128, because
- 1 times m-reduction [i] would yield (12, 70, 11198)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 3197 653070 054778 724181 296274 302920 329394 301196 556853 147268 303333 745842 181830 804924 257003 741783 866094 300513 773012 478040 894029 348762 743527 227098 272533 > 12870 [i]