Best Known (59−47, 59, s)-Nets in Base 128
(59−47, 59, 288)-Net over F128 — Constructive and digital
Digital (12, 59, 288)-net over F128, using
- t-expansion [i] based on digital (9, 59, 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
(59−47, 59, 321)-Net over F128 — Digital
Digital (12, 59, 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
(59−47, 59, 15281)-Net in Base 128 — Upper bound on s
There is no (12, 59, 15282)-net in base 128, because
- 1 times m-reduction [i] would yield (12, 58, 15282)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 165 363727 201101 569265 490052 310723 550093 656105 675139 904884 295977 492831 257087 565154 214603 997145 572846 146984 235442 038464 045232 > 12858 [i]