Best Known (57−30, 57, s)-Nets in Base 32
(57−30, 57, 174)-Net over F32 — Constructive and digital
Digital (27, 57, 174)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 20, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- 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 (5, 20, 76)-net over F32, using
(57−30, 57, 288)-Net in Base 32 — Constructive
(27, 57, 288)-net in base 32, using
- 6 times m-reduction [i] based on (27, 63, 288)-net in base 32, using
- base change [i] based on digital (9, 45, 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, 45, 288)-net over F128, using
(57−30, 57, 357)-Net over F32 — Digital
Digital (27, 57, 357)-net over F32, using
(57−30, 57, 108628)-Net in Base 32 — Upper bound on s
There is no (27, 57, 108629)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 62 167199 118784 046494 316993 704625 501802 566460 974886 208344 389108 034598 689238 201363 237808 > 3257 [i]