MinT - Best Known (102−59, 102, s)-Nets in Base 25

Best Known (102−59, 102, s)-Nets in Base 25

(102−59, 102, 288)-Net over F₂₅ — Constructive and digital

Digital (43, 102, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 102, 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]

(102−59, 102, 35926)-Net in Base 25 — Upper bound on s

There is no (43, 102, 35927)-net in base 25, because

1 times m-reduction [i] would yield (43, 101, 35927)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1556 412229 518486 198235 896588 781698 826601 952906 807797 888104 801548 662933 456551 286040 301282 142813 296910 923416 287734 026846 320923 902168 063328 537225 > 25¹⁰¹ [i]