Best Known (148−68, 148, s)-Nets in Base 4
(148−68, 148, 130)-Net over F4 — Constructive and digital
Digital (80, 148, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 74, 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
(148−68, 148, 145)-Net over F4 — Digital
Digital (80, 148, 145)-net over F4, using
(148−68, 148, 1856)-Net in Base 4 — Upper bound on s
There is no (80, 148, 1857)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 128828 400355 800600 700613 034544 808192 394274 821901 762115 615011 877120 081866 481103 912650 910208 > 4148 [i]