Best Known (34, 34+56, s)-Nets in Base 32
(34, 34+56, 128)-Net over F32 — Constructive and digital
Digital (34, 90, 128)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 31, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (3, 59, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32 (see above)
- digital (3, 31, 64)-net over F32, using
(34, 34+56, 257)-Net in Base 32 — Constructive
(34, 90, 257)-net in base 32, using
- base change [i] based on (19, 75, 257)-net in base 64, using
- 1 times m-reduction [i] based on (19, 76, 257)-net in base 64, using
- base change [i] based on digital (0, 57, 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, 57, 257)-net over F256, using
- 1 times m-reduction [i] based on (19, 76, 257)-net in base 64, using
(34, 34+56, 273)-Net over F32 — Digital
Digital (34, 90, 273)-net over F32, using
- t-expansion [i] based on digital (30, 90, 273)-net over F32, using
- net from sequence [i] based on digital (30, 272)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 30 and N(F) ≥ 273, using
- net from sequence [i] based on digital (30, 272)-sequence over F32, using
(34, 34+56, 315)-Net in Base 32
(34, 90, 315)-net in base 32, using
- base change [i] based on digital (19, 75, 315)-net over F64, using
- net from sequence [i] based on digital (19, 314)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 19 and N(F) ≥ 315, using
- net from sequence [i] based on digital (19, 314)-sequence over F64, using
(34, 34+56, 25082)-Net in Base 32 — Upper bound on s
There is no (34, 90, 25083)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2907 982605 969043 230671 301452 563011 508184 020985 201388 937980 657232 325868 894823 837564 506382 991748 459570 365413 241151 219148 701862 457028 326040 > 3290 [i]