MinT - Best Known (44, 44+51, s)-Nets in Base 25

Best Known (44, 44+51, s)-Nets in Base 25

(44, 44+51, 288)-Net over F₂₅ — Constructive and digital

Digital (44, 95, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 95, 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]

(44, 44+51, 363)-Net over F₂₅ — Digital

Digital (44, 95, 363)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 44+51, 76488)-Net in Base 25 — Upper bound on s

There is no (44, 95, 76489)-net in base 25, because

1 times m-reduction [i] would yield (44, 94, 76489)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 254953 473232 953372 203022 346513 211728 068759 103605 240152 722310 573043 614335 132133 173546 657791 536325 931428 463591 996576 084775 695753 115161 > 25⁹⁴ [i]