Best Known (108−38, 108, s)-Nets in Base 5
(108−38, 108, 252)-Net over F5 — Constructive and digital
Digital (70, 108, 252)-net over F5, using
- 12 times m-reduction [i] based on digital (70, 120, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 60, 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, 60, 126)-net over F25, using
(108−38, 108, 405)-Net over F5 — Digital
Digital (70, 108, 405)-net over F5, using
(108−38, 108, 18617)-Net in Base 5 — Upper bound on s
There is no (70, 108, 18618)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 3082 214818 147999 770539 392790 585887 523109 271011 831838 912977 983664 923714 470025 > 5108 [i]