MinT - Best Known (94−55, 94, s)-Nets in Base 25

Best Known (94−55, 94, s)-Nets in Base 25

(94−55, 94, 208)-Net over F₂₅ — Constructive and digital

Digital (39, 94, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 94, 208)-net over F₂₅, using
- net from sequence [i] based on digital (35, 207)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 35 and N(F) ≥ 208, using
    - a function field by GarcÃa and Quoos [i]

(94−55, 94, 225)-Net over F₂₅ — Digital

Digital (39, 94, 225)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(94−55, 94, 29724)-Net in Base 25 — Upper bound on s

There is no (39, 94, 29725)-net in base 25, because

1 times m-reduction [i] would yield (39, 93, 29725)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 10199 553544 711024 564812 244929 159258 104263 013430 087396 386206 702847 192111 014566 479995 430462 037600 233264 854675 618906 867891 413003 092137 > 25⁹³ [i]