Best Known (73, 73+56, s)-Nets in Base 4
(73, 73+56, 130)-Net over F4 — Constructive and digital
Digital (73, 129, 130)-net over F4, using
- 5 times m-reduction [i] based on digital (73, 134, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 67, 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, 67, 65)-net over F16, using
(73, 73+56, 154)-Net over F4 — Digital
Digital (73, 129, 154)-net over F4, using
(73, 73+56, 2214)-Net in Base 4 — Upper bound on s
There is no (73, 129, 2215)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 467677 426105 518819 193704 940595 040484 661564 058507 337984 940282 456131 869031 117708 > 4129 [i]