MinT - Best Known (46, 46+47, s)-Nets in Base 25

Best Known (46, 46+47, s)-Nets in Base 25

(46, 46+47, 288)-Net over F₂₅ — Constructive and digital

Digital (46, 93, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 93, 288)-net over F₂₅, using
- net from sequence [i] based on digital (41, 287)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 41 and N(F) ≥ 288, using
    - a function field by GarcÃa and Quoos [i]

(46, 46+47, 510)-Net over F₂₅ — Digital

Digital (46, 93, 510)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 46+47, 153451)-Net in Base 25 — Upper bound on s

There is no (46, 93, 153452)-net in base 25, because

1 times m-reduction [i] would yield (46, 92, 153452)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 407 860100 581805 477500 540950 445473 368542 177970 191233 690904 931752 308350 700443 404168 634769 097711 938836 354283 488436 536652 638321 161825 > 25⁹² [i]