Best Known (122−44, 122, s)-Nets in Base 5
(122−44, 122, 252)-Net over F5 — Constructive and digital
Digital (78, 122, 252)-net over F5, using
- 14 times m-reduction [i] based on digital (78, 136, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 68, 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, 68, 126)-net over F25, using
(122−44, 122, 401)-Net over F5 — Digital
Digital (78, 122, 401)-net over F5, using
(122−44, 122, 17001)-Net in Base 5 — Upper bound on s
There is no (78, 122, 17002)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 18 816445 971204 826229 913715 428046 881984 132615 058740 168413 124637 832072 835346 245635 562625 > 5122 [i]