Best Known (92, 92+117, s)-Nets in Base 4
(92, 92+117, 104)-Net over F4 — Constructive and digital
Digital (92, 209, 104)-net over F4, using
- t-expansion [i] based on digital (73, 209, 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+117, 144)-Net over F4 — Digital
Digital (92, 209, 144)-net over F4, using
- t-expansion [i] based on digital (91, 209, 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+117, 1032)-Net in Base 4 — Upper bound on s
There is no (92, 209, 1033)-net in base 4, because
- 1 times m-reduction [i] would yield (92, 208, 1033)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 174350 220434 023132 812794 957608 060424 934265 899535 604011 961774 198041 018621 640312 680335 726984 258552 343215 374218 161817 421460 467200 > 4208 [i]