Best Known (107−67, 107, s)-Nets in Base 32
(107−67, 107, 131)-Net over F32 — Constructive and digital
Digital (40, 107, 131)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 33, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (7, 74, 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 (0, 33, 33)-net over F32, using
(107−67, 107, 288)-Net in Base 32 — Constructive
(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
(107−67, 107, 293)-Net over F32 — Digital
Digital (40, 107, 293)-net over F32, using
- net from sequence [i] based on digital (40, 292)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 40 and N(F) ≥ 293, using
(107−67, 107, 342)-Net in Base 32
(40, 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
(107−67, 107, 29004)-Net in Base 32 — Upper bound on s
There is no (40, 107, 29005)-net in base 32, because
- 1 times m-reduction [i] would yield (40, 106, 29005)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 3517 897206 268305 352401 624356 285447 256550 224468 629556 540490 890309 979242 404349 208686 932634 493343 483962 677169 156852 342411 247734 203573 339168 605302 690190 257366 310264 > 32106 [i]