MinT - Best Known (56−49, 56, s)-Nets in Base 25

Best Known (56−49, 56, s)-Nets in Base 25

(56−49, 56, 66)-Net over F₂₅ — Constructive and digital

Digital (7, 56, 66)-net over F₂₅, using

t-expansion [i] based on digital (4, 56, 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]

(56−49, 56, 640)-Net in Base 25 — Upper bound on s

There is no (7, 56, 641)-net in base 25, because

1 times m-reduction [i] would yield (7, 55, 641)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 78955 904746 225935 566551 044018 664373 398396 279501 901127 746452 989082 532431 650625 > 25⁵⁵ [i]