Best Known (65−42, 65, s)-Nets in Base 32
(65−42, 65, 120)-Net over F32 — Constructive and digital
Digital (23, 65, 120)-net over F32, using
- t-expansion [i] based on digital (11, 65, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
(65−42, 65, 185)-Net over F32 — Digital
Digital (23, 65, 185)-net over F32, using
- t-expansion [i] based on digital (21, 65, 185)-net over F32, using
- net from sequence [i] based on digital (21, 184)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 21 and N(F) ≥ 185, using
- net from sequence [i] based on digital (21, 184)-sequence over F32, using
(65−42, 65, 192)-Net in Base 32 — Constructive
(23, 65, 192)-net in base 32, using
- 5 times m-reduction [i] based on (23, 70, 192)-net in base 32, using
- base change [i] based on digital (3, 50, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 50, 192)-net over F128, using
(65−42, 65, 257)-Net in Base 32
(23, 65, 257)-net in base 32, using
- 1 times m-reduction [i] based on (23, 66, 257)-net in base 32, using
- base change [i] based on digital (12, 55, 257)-net over F64, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 12 and N(F) ≥ 257, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- base change [i] based on digital (12, 55, 257)-net over F64, using
(65−42, 65, 12751)-Net in Base 32 — Upper bound on s
There is no (23, 65, 12752)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 68 395555 702922 344199 460346 877857 511900 716687 522638 011075 569038 361370 294651 377263 490628 591029 816108 > 3265 [i]