MinT - Best Known (45, 45+29, s)-Nets in Base 25

Best Known (45, 45+29, s)-Nets in Base 25

(45, 45+29, 288)-Net over F₂₅ — Constructive and digital

Digital (45, 74, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 74, 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+29, 2344)-Net over F₂₅ — Digital

Digital (45, 74, 2344)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(45, 45+29, 4903480)-Net in Base 25 — Upper bound on s

There is no (45, 74, 4903481)-net in base 25, because

1 times m-reduction [i] would yield (45, 73, 4903481)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1 121039 126596 046374 050532 237813 333889 190439 933418 993281 070961 325806 091954 091812 491167 514944 167705 351825 > 25⁷³ [i]