Best Known (75−28, 75, s)-Nets in Base 4
(75−28, 75, 130)-Net over F4 — Constructive and digital
Digital (47, 75, 130)-net over F4, using
- 7 times m-reduction [i] based on digital (47, 82, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 41, 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, 41, 65)-net over F16, using
(75−28, 75, 166)-Net over F4 — Digital
Digital (47, 75, 166)-net over F4, using
(75−28, 75, 3374)-Net in Base 4 — Upper bound on s
There is no (47, 75, 3375)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1429 486716 776613 512018 686121 352222 190777 275901 > 475 [i]