MinT - Best Known (83−37, 83, s)-Nets in Base 25

Best Known (83−37, 83, s)-Nets in Base 25

(83−37, 83, 288)-Net over F₂₅ — Constructive and digital

Digital (46, 83, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 83, 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]

(83−37, 83, 1012)-Net over F₂₅ — Digital

Digital (46, 83, 1012)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(83−37, 83, 735032)-Net in Base 25 — Upper bound on s

There is no (46, 83, 735033)-net in base 25, because

1 times m-reduction [i] would yield (46, 82, 735033)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 4 276443 934811 122510 804128 862909 632038 123807 917302 430748 864255 006109 453444 445852 593416 808190 038288 835814 381676 922225 > 25⁸² [i]