Best Known (68, 68+44, s)-Nets in Base 5
(68, 68+44, 252)-Net over F5 — Constructive and digital
Digital (68, 112, 252)-net over F5, using
- 4 times m-reduction [i] based on digital (68, 116, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 58, 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, 58, 126)-net over F25, using
(68, 68+44, 268)-Net over F5 — Digital
Digital (68, 112, 268)-net over F5, using
(68, 68+44, 8172)-Net in Base 5 — Upper bound on s
There is no (68, 112, 8173)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1 930275 246364 276315 038212 838408 747155 437966 034049 368468 073937 043696 541332 283721 > 5112 [i]