MinT - Best Known (49−43, 49, s)-Nets in Base 25

Best Known (49−43, 49, s)-Nets in Base 25

(49−43, 49, 66)-Net over F₂₅ — Constructive and digital

Digital (6, 49, 66)-net over F₂₅, using

t-expansion [i] based on digital (4, 49, 66)-net over F₂₅, using
- net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]

(49−43, 49, 556)-Net in Base 25 — Upper bound on s

There is no (6, 49, 557)-net in base 25, because

1 times m-reduction [i] would yield (6, 48, 557)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 13 020468 560308 871117 842181 328511 533279 256133 035781 379127 943843 473945 > 25⁴⁸ [i]