Best Known (40, 68, s)-Nets in Base 4
(40, 68, 130)-Net over F4 — Constructive and digital
Digital (40, 68, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 34, 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
(40, 68, 1681)-Net in Base 4 — Upper bound on s
There is no (40, 68, 1682)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 87293 614664 360100 378893 308300 230860 201800 > 468 [i]