Best Known (78, 78+66, s)-Nets in Base 4
(78, 78+66, 130)-Net over F4 — Constructive and digital
Digital (78, 144, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 72, 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
(78, 78+66, 142)-Net over F4 — Digital
Digital (78, 144, 142)-net over F4, using
(78, 78+66, 1832)-Net in Base 4 — Upper bound on s
There is no (78, 144, 1833)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 500 140119 404709 462053 570002 148638 640737 029573 919792 589978 200799 215018 983029 704125 299020 > 4144 [i]