Best Known (74, 124, s)-Nets in Base 4
(74, 124, 130)-Net over F4 — Constructive and digital
Digital (74, 124, 130)-net over F4, using
- 12 times m-reduction [i] based on digital (74, 136, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 68, 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
- trace code for nets [i] based on digital (6, 68, 65)-net over F16, using
(74, 124, 190)-Net over F4 — Digital
Digital (74, 124, 190)-net over F4, using
(74, 124, 3266)-Net in Base 4 — Upper bound on s
There is no (74, 124, 3267)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 455 323125 044370 406951 124076 090303 354992 924305 147451 511135 944549 718997 884784 > 4124 [i]