Best Known (69, 69+47, s)-Nets in Base 5
(69, 69+47, 252)-Net over F5 — Constructive and digital
Digital (69, 116, 252)-net over F5, using
- 2 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+47, 7349)-Net in Base 5 — Upper bound on s
There is no (69, 116, 7350)-net in base 5, because
- 1 times m-reduction [i] would yield (69, 115, 7350)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 241 108888 999128 449945 293896 041744 666097 076990 139663 745730 570930 580087 453850 481401 > 5115 [i]