Best Known (55−34, 55, s)-Nets in Base 32
(55−34, 55, 120)-Net over F32 — Constructive and digital
Digital (21, 55, 120)-net over F32, using
- t-expansion [i] based on digital (11, 55, 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
(55−34, 55, 185)-Net over F32 — Digital
Digital (21, 55, 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
(55−34, 55, 257)-Net in Base 32 — Constructive
(21, 55, 257)-net in base 32, using
- 1 times m-reduction [i] based on (21, 56, 257)-net in base 32, using
- base change [i] based on digital (0, 35, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 35, 257)-net over F256, using
(55−34, 55, 17138)-Net in Base 32 — Upper bound on s
There is no (21, 55, 17139)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 60745 553627 361181 073235 743041 552637 427609 634043 154065 870746 427429 345241 340278 616042 > 3255 [i]