Best Known (104−60, 104, s)-Nets in Base 32
(104−60, 104, 196)-Net over F32 — Constructive and digital
Digital (44, 104, 196)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 37, 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 (7, 67, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 37, 98)-net over F32, using
(104−60, 104, 288)-Net in Base 32 — Constructive
(44, 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
(104−60, 104, 325)-Net over F32 — Digital
Digital (44, 104, 325)-net over F32, using
- net from sequence [i] based on digital (44, 324)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 44 and N(F) ≥ 325, using
(104−60, 104, 425)-Net in Base 32
(44, 104, 425)-net in base 32, using
- 4 times m-reduction [i] based on (44, 108, 425)-net in base 32, using
- base change [i] based on digital (26, 90, 425)-net over F64, using
- net from sequence [i] based on digital (26, 424)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 26 and N(F) ≥ 425, using
- net from sequence [i] based on digital (26, 424)-sequence over F64, using
- base change [i] based on digital (26, 90, 425)-net over F64, using
(104−60, 104, 64146)-Net in Base 32 — Upper bound on s
There is no (44, 104, 64147)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 3 432593 244686 368387 960628 194462 042397 534867 308736 188888 528574 899569 566159 662324 322816 212308 151247 276479 630414 972974 817307 590064 579004 715765 522980 532495 056672 > 32104 [i]