Best Known (44, 44+32, s)-Nets in Base 4
(44, 44+32, 130)-Net over F4 — Constructive and digital
Digital (44, 76, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 38, 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
(44, 44+32, 1628)-Net in Base 4 — Upper bound on s
There is no (44, 76, 1629)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 5733 520254 911997 455056 959799 458012 803419 548847 > 476 [i]