MinT - Best Known (49−27, 49, s)-Nets in Base 25

Best Known (49−27, 49, s)-Nets in Base 25

(49−27, 49, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 49, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 49, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(49−27, 49, 195)-Net over F₂₅ — Digital

Digital (22, 49, 195)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(49−27, 49, 34256)-Net in Base 25 — Upper bound on s

There is no (22, 49, 34257)-net in base 25, because

1 times m-reduction [i] would yield (22, 48, 34257)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 12 626560 148115 529254 113658 629765 856236 504642 033154 219113 256763 821625 > 25⁴⁸ [i]