Best Known (41, 41+60, s)-Nets in Base 32
(41, 41+60, 162)-Net over F32 — Constructive and digital
Digital (41, 101, 162)-net over F32, using
- 2 times m-reduction [i] based on digital (41, 103, 162)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 34, 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 (7, 69, 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 (3, 34, 64)-net over F32, using
- (u, u+v)-construction [i] based on
(41, 41+60, 288)-Net in Base 32 — Constructive
(41, 101, 288)-net in base 32, using
- t-expansion [i] based on (40, 101, 288)-net in base 32, using
- 7 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
- 7 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
(41, 41+60, 308)-Net over F32 — Digital
Digital (41, 101, 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+60, 342)-Net in Base 32
(41, 101, 342)-net in base 32, using
- t-expansion [i] based on (38, 101, 342)-net in base 32, using
- 7 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
- 7 times m-reduction [i] based on (38, 108, 342)-net in base 32, using
(41, 41+60, 45354)-Net in Base 32 — Upper bound on s
There is no (41, 101, 45355)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 104 806473 785674 342361 302065 525829 628061 080442 418684 554810 119244 650602 289596 162470 478023 918772 878252 784309 219251 579791 662298 580885 899274 449853 463858 406232 > 32101 [i]