Best Known (59−51, 59, s)-Nets in Base 128
(59−51, 59, 216)-Net over F128 — Constructive and digital
Digital (8, 59, 216)-net over F128, using
- t-expansion [i] based on digital (5, 59, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
(59−51, 59, 257)-Net in Base 128 — Constructive
(8, 59, 257)-net in base 128, using
- 5 times m-reduction [i] based on (8, 64, 257)-net in base 128, using
- base change [i] based on digital (0, 56, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 56, 257)-net over F256, using
(59−51, 59, 276)-Net over F128 — Digital
Digital (8, 59, 276)-net over F128, using
- net from sequence [i] based on digital (8, 275)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 8 and N(F) ≥ 276, using
(59−51, 59, 6190)-Net in Base 128 — Upper bound on s
There is no (8, 59, 6191)-net in base 128, because
- 1 times m-reduction [i] would yield (8, 58, 6191)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 165 893135 949445 009112 803973 793983 427661 533024 858809 941901 619705 578108 994556 727681 479472 948245 042300 504309 702180 194401 104332 > 12858 [i]