MinT - Best Known (47, 84, s)-Nets in Base 25

Best Known (47, 84, s)-Nets in Base 25

(47, 84, 288)-Net over F₂₅ — Constructive and digital

Digital (47, 84, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 84, 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, 84, 1105)-Net over F₂₅ — Digital

Digital (47, 84, 1105)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 84, 878963)-Net in Base 25 — Upper bound on s

There is no (47, 84, 878964)-net in base 25, because

1 times m-reduction [i] would yield (47, 83, 878964)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 106 911193 926387 223454 165417 811013 486131 689952 661474 877626 120743 056487 972011 326292 182038 762966 299586 994797 893749 744705 > 25⁸³ [i]