MinT - Best Known (45, 45+61, s)-Nets in Base 25

Best Known (45, 45+61, s)-Nets in Base 25

(45, 45+61, 288)-Net over F₂₅ — Constructive and digital

Digital (45, 106, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 106, 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]

(45, 45+61, 39191)-Net in Base 25 — Upper bound on s

There is no (45, 106, 39192)-net in base 25, because

1 times m-reduction [i] would yield (45, 105, 39192)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 607 903030 945958 994001 911718 715870 194284 700246 752497 036884 897384 126555 042987 519090 711989 193745 455310 745470 669349 820480 841919 374436 244992 268148 903041 > 25¹⁰⁵ [i]