Best Known (129−54, 129, s)-Nets in Base 5
(129−54, 129, 252)-Net over F5 — Constructive and digital
Digital (75, 129, 252)-net over F5, using
- 1 times m-reduction [i] based on digital (75, 130, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 65, 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, 65, 126)-net over F25, using
(129−54, 129, 5948)-Net in Base 5 — Upper bound on s
There is no (75, 129, 5949)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1 470423 600307 523100 403433 638271 374953 882440 347772 734056 848652 941589 974899 517003 832815 468109 > 5129 [i]