Best Known (114−40, 114, s)-Nets in Base 5
(114−40, 114, 252)-Net over F5 — Constructive and digital
Digital (74, 114, 252)-net over F5, using
- 14 times m-reduction [i] based on digital (74, 128, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 64, 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, 64, 126)-net over F25, using
(114−40, 114, 427)-Net over F5 — Digital
Digital (74, 114, 427)-net over F5, using
(114−40, 114, 20001)-Net in Base 5 — Upper bound on s
There is no (74, 114, 20002)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 48 176625 915137 872955 617657 180346 005163 097624 633734 298529 813962 358545 508036 194625 > 5114 [i]