Best Known (68, 68+48, s)-Nets in Base 5
(68, 68+48, 252)-Net over F5 — Constructive and digital
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
(68, 68+48, 5839)-Net in Base 5 — Upper bound on s
There is no (68, 116, 5840)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1207 246138 892190 027230 306072 358692 108317 735420 652918 315291 092212 445516 658768 738305 > 5116 [i]