Best Known (69−41, 69, s)-Nets in Base 128
(69−41, 69, 408)-Net over F128 — Constructive and digital
Digital (28, 69, 408)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 23, 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 (5, 46, 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
- digital (3, 23, 192)-net over F128, using
(69−41, 69, 432)-Net in Base 128 — Constructive
(28, 69, 432)-net in base 128, using
- (u, u+v)-construction [i] based on
- (3, 23, 257)-net in base 128, using
- 1 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
- 1 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
- digital (5, 46, 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
- (3, 23, 257)-net in base 128, using
(69−41, 69, 577)-Net over F128 — Digital
Digital (28, 69, 577)-net over F128, using
- net from sequence [i] based on digital (28, 576)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 28 and N(F) ≥ 577, using
(69−41, 69, 955019)-Net in Base 128 — Upper bound on s
There is no (28, 69, 955020)-net in base 128, because
- 1 times m-reduction [i] would yield (28, 68, 955020)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 195113 342742 146137 541409 568494 377247 326665 437327 104787 068882 951480 070875 956960 693172 598341 890355 786492 664859 032898 059826 666523 012824 028330 399728 > 12868 [i]