Best Known (78−52, 78, s)-Nets in Base 32
(78−52, 78, 120)-Net over F32 — Constructive and digital
Digital (26, 78, 120)-net over F32, using
- t-expansion [i] based on digital (11, 78, 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
(78−52, 78, 192)-Net in Base 32 — Constructive
(26, 78, 192)-net in base 32, using
- 321 times duplication [i] based on (25, 77, 192)-net in base 32, using
- base change [i] based on digital (3, 55, 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, 55, 192)-net over F128, using
(78−52, 78, 225)-Net over F32 — Digital
Digital (26, 78, 225)-net over F32, using
- t-expansion [i] based on digital (24, 78, 225)-net over F32, using
- net from sequence [i] based on digital (24, 224)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 24 and N(F) ≥ 225, using
- net from sequence [i] based on digital (24, 224)-sequence over F32, using
(78−52, 78, 257)-Net in Base 32
(26, 78, 257)-net in base 32, using
- 6 times m-reduction [i] based on (26, 84, 257)-net in base 32, using
- base change [i] based on digital (12, 70, 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, 70, 257)-net over F64, using
(78−52, 78, 11139)-Net in Base 32 — Upper bound on s
There is no (26, 78, 11140)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2525 274835 324845 090068 638511 361968 506184 967197 203225 903462 170686 509378 294841 067824 067990 399820 052543 084447 777388 974672 > 3278 [i]