Best Known (18, 18+23, s)-Nets in Base 25
(18, 18+23, 126)-Net over F25 — Constructive and digital
Digital (18, 41, 126)-net over F25, using
- t-expansion [i] based on digital (10, 41, 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
(18, 18+23, 158)-Net over F25 — Digital
Digital (18, 41, 158)-net over F25, using
(18, 18+23, 24781)-Net in Base 25 — Upper bound on s
There is no (18, 41, 24782)-net in base 25, because
- 1 times m-reduction [i] would yield (18, 40, 24782)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 82 740826 045923 998728 538029 951512 204066 908496 009652 993585 > 2540 [i]