Best Known (69, 69+44, s)-Nets in Base 5
(69, 69+44, 252)-Net over F5 — Constructive and digital
Digital (69, 113, 252)-net over F5, using
- 5 times m-reduction [i] based on digital (69, 118, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 59, 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, 59, 126)-net over F25, using
(69, 69+44, 279)-Net over F5 — Digital
Digital (69, 113, 279)-net over F5, using
(69, 69+44, 8793)-Net in Base 5 — Upper bound on s
There is no (69, 113, 8794)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 9 638553 189014 621983 165262 711531 626131 352584 514903 041331 194400 463986 552008 806785 > 5113 [i]