Best Known (104−63, 104, s)-Nets in Base 32
(104−63, 104, 162)-Net over F32 — Constructive and digital
Digital (41, 104, 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, 70, 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
(104−63, 104, 288)-Net in Base 32 — Constructive
(41, 104, 288)-net in base 32, using
- t-expansion [i] based on (40, 104, 288)-net in base 32, using
- 4 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
- 4 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
(104−63, 104, 308)-Net over F32 — Digital
Digital (41, 104, 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
(104−63, 104, 342)-Net in Base 32
(41, 104, 342)-net in base 32, using
- t-expansion [i] based on (38, 104, 342)-net in base 32, using
- 4 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
- 4 times m-reduction [i] based on (38, 108, 342)-net in base 32, using
(104−63, 104, 40131)-Net in Base 32 — Upper bound on s
There is no (41, 104, 40132)-net in base 32, because
- 1 times m-reduction [i] would yield (41, 103, 40132)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 107342 487828 503912 951587 577509 121245 163688 590700 265520 430888 989641 651941 511995 453048 756165 642589 748661 445581 626839 262938 704054 490202 628055 161900 647903 953008 > 32103 [i]