MinT - Best Known (79−35, 79, s)-Nets in Base 25

Best Known (79−35, 79, s)-Nets in Base 25

(79−35, 79, 288)-Net over F₂₅ — Constructive and digital

Digital (44, 79, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 79, 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]

(79−35, 79, 1016)-Net over F₂₅ — Digital

Digital (44, 79, 1016)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(79−35, 79, 775901)-Net in Base 25 — Upper bound on s

There is no (44, 79, 775902)-net in base 25, because

1 times m-reduction [i] would yield (44, 78, 775902)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 10 947684 396964 319323 739286 712724 772303 331875 798322 295052 969941 721874 875758 814370 621863 880663 594648 647661 519825 > 25⁷⁸ [i]