Best Known (132−52, 132, s)-Nets in Base 4
(132−52, 132, 130)-Net over F4 — Constructive and digital
Digital (80, 132, 130)-net over F4, using
- 16 times m-reduction [i] based on digital (80, 148, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 74, 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, 74, 65)-net over F16, using
(132−52, 132, 217)-Net over F4 — Digital
Digital (80, 132, 217)-net over F4, using
(132−52, 132, 3985)-Net in Base 4 — Upper bound on s
There is no (80, 132, 3986)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 29 729330 947078 321565 150423 433062 672895 249981 639958 740554 241117 544715 916807 281344 > 4132 [i]