Best Known (61−33, 61, s)-Nets in Base 128
(61−33, 61, 480)-Net over F128 — Constructive and digital
Digital (28, 61, 480)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 19, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (9, 42, 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
- digital (3, 19, 192)-net over F128, using
(61−33, 61, 545)-Net in Base 128 — Constructive
(28, 61, 545)-net in base 128, using
- (u, u+v)-construction [i] based on
- (3, 19, 257)-net in base 128, using
- 5 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
- base change [i] based on digital (0, 21, 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, 21, 257)-net over F256, using
- 5 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
- digital (9, 42, 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
- (3, 19, 257)-net in base 128, using
(61−33, 61, 1063)-Net over F128 — Digital
Digital (28, 61, 1063)-net over F128, using
(61−33, 61, 4273381)-Net in Base 128 — Upper bound on s
There is no (28, 61, 4273382)-net in base 128, because
- 1 times m-reduction [i] would yield (28, 60, 4273382)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 2 707695 378761 206816 352211 604218 433027 192678 958103 209562 227370 506656 957271 726395 932547 821913 122700 151944 489840 183601 555431 543410 > 12860 [i]