Best Known (41, 41+57, s)-Nets in Base 32
(41, 41+57, 174)-Net over F32 — Constructive and digital
Digital (41, 98, 174)-net over F32, using
- 1 times m-reduction [i] based on digital (41, 99, 174)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 34, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- digital (7, 65, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (5, 34, 76)-net over F32, using
- (u, u+v)-construction [i] based on
(41, 41+57, 288)-Net in Base 32 — Constructive
(41, 98, 288)-net in base 32, using
- t-expansion [i] based on (40, 98, 288)-net in base 32, using
- 10 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
- base change [i] based on (22, 90, 288)-net in base 64, using
- 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on digital (9, 78, 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
- base change [i] based on digital (9, 78, 288)-net over F128, using
- 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on (22, 90, 288)-net in base 64, using
- 10 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
(41, 41+57, 308)-Net over F32 — Digital
Digital (41, 98, 308)-net over F32, using
- net from sequence [i] based on digital (41, 307)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 41 and N(F) ≥ 308, using
(41, 41+57, 342)-Net in Base 32
(41, 98, 342)-net in base 32, using
- t-expansion [i] based on (38, 98, 342)-net in base 32, using
- 10 times m-reduction [i] based on (38, 108, 342)-net in base 32, using
- base change [i] based on digital (20, 90, 342)-net over F64, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 20 and N(F) ≥ 342, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
- base change [i] based on digital (20, 90, 342)-net over F64, using
- 10 times m-reduction [i] based on (38, 108, 342)-net in base 32, using
(41, 41+57, 59677)-Net in Base 32 — Upper bound on s
There is no (41, 98, 59678)-net in base 32, because
- 1 times m-reduction [i] would yield (41, 97, 59678)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 99 935604 321109 112287 022816 836565 626214 277589 441580 315659 174680 643335 336351 854582 106554 653801 348823 778091 029523 419351 660145 955798 557025 164630 421997 > 3297 [i]