Best Known (142−53, 142, s)-Nets in Base 4
(142−53, 142, 130)-Net over F4 — Constructive and digital
Digital (89, 142, 130)-net over F4, using
- 24 times m-reduction [i] based on digital (89, 166, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 83, 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, 83, 65)-net over F16, using
(142−53, 142, 276)-Net over F4 — Digital
Digital (89, 142, 276)-net over F4, using
(142−53, 142, 6453)-Net in Base 4 — Upper bound on s
There is no (89, 142, 6454)-net in base 4, because
- 1 times m-reduction [i] would yield (89, 141, 6454)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 7 798515 430877 133372 824585 928590 207260 846925 857960 051857 701684 469244 481729 094417 112984 > 4141 [i]