MinT - Best Known (40, 40+49, s)-Nets in Base 25

Best Known (40, 40+49, s)-Nets in Base 25

(40, 40+49, 208)-Net over F₂₅ — Constructive and digital

Digital (40, 89, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 89, 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]

(40, 40+49, 299)-Net over F₂₅ — Digital

Digital (40, 89, 299)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 40+49, 54554)-Net in Base 25 — Upper bound on s

There is no (40, 89, 54555)-net in base 25, because

1 times m-reduction [i] would yield (40, 88, 54555)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1044 194438 862931 582806 745207 543893 521979 331281 940666 134563 395451 653198 001630 487218 121338 608514 144713 352339 897900 154105 441985 > 25⁸⁸ [i]