Best Known (72−26, 72, s)-Nets in Base 5
(72−26, 72, 252)-Net over F5 — Constructive and digital
Digital (46, 72, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 36, 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
(72−26, 72, 272)-Net over F5 — Digital
Digital (46, 72, 272)-net over F5, using
(72−26, 72, 10524)-Net in Base 5 — Upper bound on s
There is no (46, 72, 10525)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 212 004483 993168 444008 215482 163185 921580 159302 904581 > 572 [i]