Best Known (142−60, 142, s)-Nets in Base 5
(142−60, 142, 252)-Net over F5 — Constructive and digital
Digital (82, 142, 252)-net over F5, using
- 2 times m-reduction [i] based on digital (82, 144, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 72, 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, 72, 126)-net over F25, using
(142−60, 142, 6104)-Net in Base 5 — Upper bound on s
There is no (82, 142, 6105)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1801 009494 903092 223217 468806 494587 081310 886186 585499 914598 808544 831754 233535 952569 526845 004566 774185 > 5142 [i]