MinT - Best Known (100−53, 100, s)-Nets in Base 25

Best Known (100−53, 100, s)-Nets in Base 25

(100−53, 100, 288)-Net over F₂₅ — Constructive and digital

Digital (47, 100, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 100, 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]

(100−53, 100, 407)-Net over F₂₅ — Digital

Digital (47, 100, 407)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(100−53, 100, 92457)-Net in Base 25 — Upper bound on s

There is no (47, 100, 92458)-net in base 25, because

1 times m-reduction [i] would yield (47, 99, 92458)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 2 489366 506250 106600 684484 549688 477118 902385 029040 180741 257563 772233 279595 251123 536095 449905 035174 581550 339615 503162 835824 084848 295535 588641 > 25⁹⁹ [i]