Best Known (112−42, 112, s)-Nets in Base 5
(112−42, 112, 252)-Net over F5 — Constructive and digital
Digital (70, 112, 252)-net over F5, using
- 8 times m-reduction [i] based on digital (70, 120, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 60, 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, 60, 126)-net over F25, using
(112−42, 112, 320)-Net over F5 — Digital
Digital (70, 112, 320)-net over F5, using
(112−42, 112, 11579)-Net in Base 5 — Upper bound on s
There is no (70, 112, 11580)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1 926604 922245 308315 890757 070488 274981 538882 602552 036799 620761 632675 192919 300465 > 5112 [i]