Best Known (92, 92+56, s)-Nets in Base 4
(92, 92+56, 130)-Net over F4 — Constructive and digital
Digital (92, 148, 130)-net over F4, using
- 24 times m-reduction [i] based on digital (92, 172, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 86, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 86, 65)-net over F16, using
(92, 92+56, 274)-Net over F4 — Digital
Digital (92, 148, 274)-net over F4, using
(92, 92+56, 5707)-Net in Base 4 — Upper bound on s
There is no (92, 148, 5708)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 127431 845936 121012 683430 370315 889891 896574 922420 195708 462558 583177 748554 825527 891389 086480 > 4148 [i]