Best Known (88−38, 88, s)-Nets in Base 4
(88−38, 88, 130)-Net over F4 — Constructive and digital
Digital (50, 88, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 44, 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
(88−38, 88, 1608)-Net in Base 4 — Upper bound on s
There is no (50, 88, 1609)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 96106 764052 610361 002655 208733 996340 526775 241624 099232 > 488 [i]