Best Known (100−62, 100, s)-Nets in Base 32
(100−62, 100, 131)-Net over F32 — Constructive and digital
Digital (38, 100, 131)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 31, 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, 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 (0, 31, 33)-net over F32, using
(100−62, 100, 216)-Net in Base 32 — Constructive
(38, 100, 216)-net in base 32, using
- t-expansion [i] based on (36, 100, 216)-net in base 32, using
- 8 times m-reduction [i] based on (36, 108, 216)-net in base 32, using
- base change [i] based on (18, 90, 216)-net in base 64, using
- 1 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
- base change [i] based on digital (5, 78, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- base change [i] based on digital (5, 78, 216)-net over F128, using
- 1 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
- base change [i] based on (18, 90, 216)-net in base 64, using
- 8 times m-reduction [i] based on (36, 108, 216)-net in base 32, using
(100−62, 100, 291)-Net over F32 — Digital
Digital (38, 100, 291)-net over F32, using
- net from sequence [i] based on digital (38, 290)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 38 and N(F) ≥ 291, using
(100−62, 100, 342)-Net in Base 32
(38, 100, 342)-net in base 32, using
- 8 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
(100−62, 100, 28691)-Net in Base 32 — Upper bound on s
There is no (38, 100, 28692)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 3 275524 847003 067221 790209 286957 214535 159690 885513 761613 260688 562134 258110 622469 159733 831103 948788 786198 502077 984094 732470 938952 151438 105411 126025 159680 > 32100 [i]