Best Known (134−57, 134, s)-Nets in Base 5
(134−57, 134, 252)-Net over F5 — Constructive and digital
Digital (77, 134, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 67, 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
(134−57, 134, 5882)-Net in Base 5 — Upper bound on s
There is no (77, 134, 5883)-net in base 5, because
- 1 times m-reduction [i] would yield (77, 133, 5883)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 921 625150 356834 712944 831306 006984 931756 609870 570939 144835 171640 003699 831044 882129 872020 951825 > 5133 [i]