Best Known (93, 93+56, s)-Nets in Base 4
(93, 93+56, 130)-Net over F4 — Constructive and digital
Digital (93, 149, 130)-net over F4, using
- 25 times m-reduction [i] based on digital (93, 174, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 87, 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, 87, 65)-net over F16, using
(93, 93+56, 281)-Net over F4 — Digital
Digital (93, 149, 281)-net over F4, using
(93, 93+56, 5998)-Net in Base 4 — Upper bound on s
There is no (93, 149, 5999)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 510025 210946 206172 115425 729831 783451 732083 741613 115558 400221 783198 701276 717865 002230 315482 > 4149 [i]