MinT - Best Known (44, 44+33, s)-Nets in Base 25

Best Known (44, 44+33, s)-Nets in Base 25

(44, 44+33, 288)-Net over F₂₅ — Constructive and digital

Digital (44, 77, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 77, 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+33, 1248)-Net over F₂₅ — Digital

Digital (44, 77, 1248)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 44+33, 1237484)-Net in Base 25 — Upper bound on s

There is no (44, 77, 1237485)-net in base 25, because

1 times m-reduction [i] would yield (44, 76, 1237485)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 17516 414965 865733 879813 589235 256326 447784 468134 558518 106905 506112 959508 404862 179690 857540 951612 314124 098945 > 25⁷⁶ [i]