Best Known (135−57, 135, s)-Nets in Base 5
(135−57, 135, 252)-Net over F5 — Constructive and digital
Digital (78, 135, 252)-net over F5, using
- 1 times m-reduction [i] based on digital (78, 136, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 68, 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, 68, 126)-net over F25, using
(135−57, 135, 6231)-Net in Base 5 — Upper bound on s
There is no (78, 135, 6232)-net in base 5, because
- 1 times m-reduction [i] would yield (78, 134, 6232)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 4602 520491 333098 744146 155491 869481 115783 273542 094296 792062 584094 799247 770070 202447 711960 443905 > 5134 [i]