Best Known (28, 28+59, s)-Nets in Base 32
(28, 28+59, 120)-Net over F32 — Constructive and digital
Digital (28, 87, 120)-net over F32, using
- t-expansion [i] based on digital (11, 87, 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
(28, 28+59, 177)-Net in Base 32 — Constructive
(28, 87, 177)-net in base 32, using
- t-expansion [i] based on (25, 87, 177)-net in base 32, using
- 21 times m-reduction [i] based on (25, 108, 177)-net in base 32, using
- base change [i] based on digital (7, 90, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- base change [i] based on digital (7, 90, 177)-net over F64, using
- 21 times m-reduction [i] based on (25, 108, 177)-net in base 32, using
(28, 28+59, 257)-Net over F32 — Digital
Digital (28, 87, 257)-net over F32, using
- net from sequence [i] based on digital (28, 256)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 28 and N(F) ≥ 257, using
(28, 28+59, 10932)-Net in Base 32 — Upper bound on s
There is no (28, 87, 10933)-net in base 32, because
- 1 times m-reduction [i] would yield (28, 86, 10933)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 2777 025437 589008 791073 211893 659632 326014 889211 767878 562988 951900 536807 867367 884227 967435 064281 434481 462291 757047 957430 602611 714336 > 3286 [i]