Best Known (107−42, 107, s)-Nets in Base 5
(107−42, 107, 252)-Net over F5 — Constructive and digital
Digital (65, 107, 252)-net over F5, using
- 3 times m-reduction [i] based on digital (65, 110, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 55, 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, 55, 126)-net over F25, using
(107−42, 107, 259)-Net over F5 — Digital
Digital (65, 107, 259)-net over F5, using
(107−42, 107, 7888)-Net in Base 5 — Upper bound on s
There is no (65, 107, 7889)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 616 563324 639046 927820 055298 740771 220438 271011 484328 967882 984809 422846 351925 > 5107 [i]