MinT - Best Known (47, 47+56, s)-Nets in Base 25

Best Known (47, 47+56, s)-Nets in Base 25

(47, 47+56, 288)-Net over F₂₅ — Constructive and digital

Digital (47, 103, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 103, 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+56, 360)-Net over F₂₅ — Digital

Digital (47, 103, 360)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 47+56, 65330)-Net in Base 25 — Upper bound on s

There is no (47, 103, 65331)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 972397 898792 558346 996206 776137 684453 715988 542014 051846 210071 371497 523191 620531 821448 092994 180659 067883 155924 044827 276345 686843 891565 521653 012705 > 25¹⁰³ [i]