Best Known (9, 9+47, s)-Nets in Base 128
(9, 9+47, 288)-Net over F128 — Constructive and digital
Digital (9, 56, 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
(9, 9+47, 321)-Net in Base 128
(9, 56, 321)-net in base 128, using
- base change [i] based on digital (2, 49, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
(9, 9+47, 8110)-Net in Base 128 — Upper bound on s
There is no (9, 56, 8111)-net in base 128, because
- 1 times m-reduction [i] would yield (9, 55, 8111)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 78 969411 570968 429867 483650 790120 236851 513923 919076 841948 032186 446796 250513 063052 448754 305209 871291 270441 861257 513488 > 12855 [i]