Best Known (88−48, 88, s)-Nets in Base 32
(88−48, 88, 202)-Net over F32 — Constructive and digital
Digital (40, 88, 202)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 31, 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 (9, 57, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- digital (7, 31, 98)-net over F32, using
(88−48, 88, 288)-Net in Base 32 — Constructive
(40, 88, 288)-net in base 32, using
- 20 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
(88−48, 88, 389)-Net over F32 — Digital
Digital (40, 88, 389)-net over F32, using
(88−48, 88, 408)-Net in Base 32
(40, 88, 408)-net in base 32, using
- 2 times m-reduction [i] based on (40, 90, 408)-net in base 32, using
- base change [i] based on digital (25, 75, 408)-net over F64, using
- net from sequence [i] based on digital (25, 407)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 25 and N(F) ≥ 408, using
- net from sequence [i] based on digital (25, 407)-sequence over F64, using
- base change [i] based on digital (25, 75, 408)-net over F64, using
(88−48, 88, 104431)-Net in Base 32 — Upper bound on s
There is no (40, 88, 104432)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2 839266 901887 991951 886275 940703 295552 811698 628745 819838 137934 444324 488004 030535 514615 945915 952218 115686 274867 216193 162996 962391 943314 > 3288 [i]