Best Known (128−48, 128, s)-Nets in Base 5
(128−48, 128, 252)-Net over F5 — Constructive and digital
Digital (80, 128, 252)-net over F5, using
- 12 times m-reduction [i] based on digital (80, 140, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 70, 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, 70, 126)-net over F25, using
(128−48, 128, 357)-Net over F5 — Digital
Digital (80, 128, 357)-net over F5, using
(128−48, 128, 13078)-Net in Base 5 — Upper bound on s
There is no (80, 128, 13079)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 294071 788867 821333 471765 470900 952806 307016 170075 084596 050690 069697 091032 847488 512660 702625 > 5128 [i]