MinT - Best Known (42, 69, s)-Nets in Base 25

Best Known (42, 69, s)-Nets in Base 25

(42, 69, 288)-Net over F₂₅ — Constructive and digital

Digital (42, 69, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 69, 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, 69, 2267)-Net over F₂₅ — Digital

Digital (42, 69, 2267)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 69, 4847255)-Net in Base 25 — Upper bound on s

There is no (42, 69, 4847256)-net in base 25, because

1 times m-reduction [i] would yield (42, 68, 4847256)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 114794 448204 379647 219444 047136 167894 127795 937932 600678 782431 560206 656689 209829 709286 253229 986625 > 25⁶⁸ [i]