Best Known (112−40, 112, s)-Nets in Base 5
(112−40, 112, 252)-Net over F5 — Constructive and digital
Digital (72, 112, 252)-net over F5, using
- 12 times m-reduction [i] based on digital (72, 124, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 62, 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, 62, 126)-net over F25, using
(112−40, 112, 391)-Net over F5 — Digital
Digital (72, 112, 391)-net over F5, using
(112−40, 112, 17025)-Net in Base 5 — Upper bound on s
There is no (72, 112, 17026)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1 926280 861824 204344 317467 347604 353862 993492 909915 327170 556915 568290 859801 155905 > 5112 [i]