MinT - Best Known (42, 42+33, s)-Nets in Base 25

Best Known (42, 42+33, s)-Nets in Base 25

(42, 42+33, 288)-Net over F₂₅ — Constructive and digital

Digital (42, 75, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 75, 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+33, 1023)-Net over F₂₅ — Digital

Digital (42, 75, 1023)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 42+33, 827552)-Net in Base 25 — Upper bound on s

There is no (42, 75, 827553)-net in base 25, because

1 times m-reduction [i] would yield (42, 74, 827553)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 28 026052 065424 867547 108274 896368 921501 870729 969641 243266 327956 929241 172452 039638 183855 027918 968805 588865 > 25⁷⁴ [i]