Best Known (92, 92+165, s)-Nets in Base 4
(92, 92+165, 104)-Net over F4 — Constructive and digital
Digital (92, 257, 104)-net over F4, using
- t-expansion [i] based on digital (73, 257, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
(92, 92+165, 144)-Net over F4 — Digital
Digital (92, 257, 144)-net over F4, using
- t-expansion [i] based on digital (91, 257, 144)-net over F4, using
- net from sequence [i] based on digital (91, 143)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 91 and N(F) ≥ 144, using
- net from sequence [i] based on digital (91, 143)-sequence over F4, using
(92, 92+165, 725)-Net in Base 4 — Upper bound on s
There is no (92, 257, 726)-net in base 4, because
- 1 times m-reduction [i] would yield (92, 256, 726)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 13471 774229 907664 360601 181482 074089 550938 778404 416302 700540 667782 982002 787986 668220 044288 855099 480062 908642 659532 539549 361876 254899 113435 471420 327167 713814 > 4256 [i]