MinT - Best Known (80−35, 80, s)-Nets in Base 25

Best Known (80−35, 80, s)-Nets in Base 25

(80−35, 80, 288)-Net over F₂₅ — Constructive and digital

Digital (45, 80, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 80, 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]

(80−35, 80, 1115)-Net over F₂₅ — Digital

Digital (45, 80, 1115)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(80−35, 80, 937647)-Net in Base 25 — Upper bound on s

There is no (45, 80, 937648)-net in base 25, because

1 times m-reduction [i] would yield (45, 79, 937648)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 273 695905 219980 486182 750144 110455 282481 657955 350629 332460 308359 847421 581141 261515 981274 107758 158871 822226 266241 > 25⁷⁹ [i]