MinT - Best Known (42, 42+31, s)-Nets in Base 25

Best Known (42, 42+31, s)-Nets in Base 25

(42, 42+31, 288)-Net over F₂₅ — Constructive and digital

Digital (42, 73, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 73, 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]

(42, 42+31, 1280)-Net over F₂₅ — Digital

Digital (42, 73, 1280)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 42+31, 1372982)-Net in Base 25 — Upper bound on s

There is no (42, 73, 1372983)-net in base 25, because

1 times m-reduction [i] would yield (42, 72, 1372983)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 44841 753989 059900 917658 617276 246701 765974 225044 431479 920899 711153 282442 280229 909982 990627 522072 505945 > 25⁷² [i]