Best Known (45−39, 45, s)-Nets in Base 128
(45−39, 45, 216)-Net over F128 — Constructive and digital
Digital (6, 45, 216)-net over F128, using
- t-expansion [i] based on digital (5, 45, 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
(45−39, 45, 243)-Net over F128 — Digital
Digital (6, 45, 243)-net over F128, using
- net from sequence [i] based on digital (6, 242)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 6 and N(F) ≥ 243, using
(45−39, 45, 257)-Net in Base 128 — Constructive
(6, 45, 257)-net in base 128, using
- 3 times m-reduction [i] based on (6, 48, 257)-net in base 128, using
- base change [i] based on digital (0, 42, 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, 42, 257)-net over F256, using
(45−39, 45, 4725)-Net in Base 128 — Upper bound on s
There is no (6, 45, 4726)-net in base 128, because
- 1 times m-reduction [i] would yield (6, 44, 4726)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 523 010554 618257 111281 350281 270575 964486 658678 570909 954547 338820 344547 804775 586451 891043 811082 > 12844 [i]