Best Known (63−36, 63, s)-Nets in Base 32
(63−36, 63, 142)-Net over F32 — Constructive and digital
Digital (27, 63, 142)-net over F32, using
- 2 times m-reduction [i] based on digital (27, 65, 142)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 20, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (7, 45, 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 (1, 20, 44)-net over F32, using
- (u, u+v)-construction [i] based on
(63−36, 63, 229)-Net over F32 — Digital
Digital (27, 63, 229)-net over F32, using
(63−36, 63, 288)-Net in Base 32 — Constructive
(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
(63−36, 63, 321)-Net in Base 32
(27, 63, 321)-net in base 32, using
- 3 times m-reduction [i] based on (27, 66, 321)-net in base 32, using
- base change [i] based on (16, 55, 321)-net in base 64, using
- 1 times m-reduction [i] based on (16, 56, 321)-net in base 64, using
- base change [i] based on digital (2, 42, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 42, 321)-net over F256, using
- 1 times m-reduction [i] based on (16, 56, 321)-net in base 64, using
- base change [i] based on (16, 55, 321)-net in base 64, using
(63−36, 63, 45155)-Net in Base 32 — Upper bound on s
There is no (27, 63, 45156)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 66775 879716 329254 050197 267090 845396 785497 539791 778729 704009 048854 878468 100266 293739 257461 280950 > 3263 [i]