Best Known (68, 68+56, s)-Nets in Base 4
(68, 68+56, 130)-Net over F4 — Constructive and digital
Digital (68, 124, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 62, 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
(68, 68+56, 132)-Net over F4 — Digital
Digital (68, 124, 132)-net over F4, using
(68, 68+56, 1723)-Net in Base 4 — Upper bound on s
There is no (68, 124, 1724)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 454 465968 246032 539973 502112 720322 269875 216723 076803 380048 221046 887982 727256 > 4124 [i]