Best Known (41, 107, s)-Nets in Base 32
(41, 107, 142)-Net over F32 — Constructive and digital
Digital (41, 107, 142)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 34, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (7, 73, 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 (1, 34, 44)-net over F32, using
(41, 107, 288)-Net in Base 32 — Constructive
(41, 107, 288)-net in base 32, using
- t-expansion [i] based on (40, 107, 288)-net in base 32, using
- 1 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
- 1 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
(41, 107, 308)-Net over F32 — Digital
Digital (41, 107, 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, 107, 342)-Net in Base 32
(41, 107, 342)-net in base 32, using
- t-expansion [i] based on (38, 107, 342)-net in base 32, using
- 1 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
- 1 times m-reduction [i] based on (38, 108, 342)-net in base 32, using
(41, 107, 32217)-Net in Base 32 — Upper bound on s
There is no (41, 107, 32218)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 112484 138346 271928 349582 411469 324610 464585 810993 220860 572228 178670 328372 352966 010638 768817 916611 637356 456028 345291 654729 679354 547513 621690 474529 841580 985408 204490 > 32107 [i]