MinT - Best Known (70−39, 70, s)-Nets in Base 25

Best Known (70−39, 70, s)-Nets in Base 25

(70−39, 70, 204)-Net over F₂₅ — Constructive and digital

Digital (31, 70, 204)-net over F₂₅, using

t-expansion [i] based on digital (30, 70, 204)-net over F₂₅, using
- net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
    - a function field by GarcÃa and Quoos [i]

(70−39, 70, 233)-Net over F₂₅ — Digital

Digital (31, 70, 233)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70−39, 70, 39411)-Net in Base 25 — Upper bound on s

There is no (31, 70, 39412)-net in base 25, because

1 times m-reduction [i] would yield (31, 69, 39412)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 2 870183 499994 465141 518375 086505 988362 474388 965682 173137 139700 029893 661980 521900 157732 693928 789025 > 25⁶⁹ [i]