Best Known (137−52, 137, s)-Nets in Base 4
(137−52, 137, 130)-Net over F4 — Constructive and digital
Digital (85, 137, 130)-net over F4, using
- 21 times m-reduction [i] based on digital (85, 158, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 79, 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, 79, 65)-net over F16, using
(137−52, 137, 253)-Net over F4 — Digital
Digital (85, 137, 253)-net over F4, using
(137−52, 137, 5209)-Net in Base 4 — Upper bound on s
There is no (85, 137, 5210)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 30410 602292 174027 086996 274496 009941 125173 797836 342848 033813 639740 414582 402502 656968 > 4137 [i]