Best Known (32, 78, s)-Nets in Base 128
(32, 78, 417)-Net over F128 — Constructive and digital
Digital (32, 78, 417)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 23, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (9, 55, 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 (0, 23, 129)-net over F128, using
(32, 78, 432)-Net in Base 128 — Constructive
(32, 78, 432)-net in base 128, using
- (u, u+v)-construction [i] based on
- (4, 27, 257)-net in base 128, using
- 5 times m-reduction [i] based on (4, 32, 257)-net in base 128, using
- base change [i] based on digital (0, 28, 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, 28, 257)-net over F256, using
- 5 times m-reduction [i] based on (4, 32, 257)-net in base 128, using
- digital (5, 51, 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
- (4, 27, 257)-net in base 128, using
(32, 78, 643)-Net over F128 — Digital
Digital (32, 78, 643)-net over F128, using
(32, 78, 1039532)-Net in Base 128 — Upper bound on s
There is no (32, 78, 1039533)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 230 345134 961375 286667 454258 662787 979999 697247 141069 525351 065319 809470 254217 227176 098968 091990 013594 009285 977955 993519 239671 131728 150524 664593 797479 703200 503109 511152 > 12878 [i]