MinT - Best Known (47, 47+47, s)-Nets in Base 25

Best Known (47, 47+47, s)-Nets in Base 25

(47, 47+47, 288)-Net over F₂₅ — Constructive and digital

Digital (47, 94, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 94, 288)-net over F₂₅, using
- net from sequence [i] based on digital (41, 287)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 41 and N(F) ≥ 288, using
    - a function field by GarcÃa and Quoos [i]

(47, 47+47, 549)-Net over F₂₅ — Digital

Digital (47, 94, 549)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 47+47, 176504)-Net in Base 25 — Upper bound on s

There is no (47, 94, 176505)-net in base 25, because

1 times m-reduction [i] would yield (47, 93, 176505)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 10196 523659 278357 776738 871069 871656 524508 561916 088703 847724 204441 411831 851471 622285 734344 771074 309505 618488 262445 317658 019739 568425 > 25⁹³ [i]