MinT - Best Known (18, 41, s)-Nets in Base 25

Best Known (18, 41, s)-Nets in Base 25

(18, 41, 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
  - Niederreiterâ€“Xing sequence constructionÂ 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]

(18, 41, 158)-Net over F₂₅ — Digital

Digital (18, 41, 158)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(18, 41, 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 25^mÂ â‰¥ 82 740826 045923 998728 538029 951512 204066 908496 009652 993585 > 25⁴⁰ [i]