Best Known (128−52, 128, s)-Nets in Base 5
(128−52, 128, 252)-Net over F5 — Constructive and digital
Digital (76, 128, 252)-net over F5, using
- 4 times m-reduction [i] based on digital (76, 132, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 66, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 66, 126)-net over F25, using
(128−52, 128, 264)-Net over F5 — Digital
Digital (76, 128, 264)-net over F5, using
(128−52, 128, 7264)-Net in Base 5 — Upper bound on s
There is no (76, 128, 7265)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 294802 761868 394695 135236 060188 808300 374699 787429 475695 994644 893924 114748 915442 045525 555385 > 5128 [i]