Best Known (132−54, 132, s)-Nets in Base 5
(132−54, 132, 252)-Net over F5 — Constructive and digital
Digital (78, 132, 252)-net over F5, using
- 4 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
(132−54, 132, 265)-Net over F5 — Digital
Digital (78, 132, 265)-net over F5, using
(132−54, 132, 7117)-Net in Base 5 — Upper bound on s
There is no (78, 132, 7118)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 183 975831 724883 649831 737560 910581 387702 021193 707402 435092 249870 625272 389533 209026 121732 442201 > 5132 [i]