MinT - Best Known (70−27, 70, s)-Nets in Base 25

Best Known (70−27, 70, s)-Nets in Base 25

(70−27, 70, 288)-Net over F₂₅ — Constructive and digital

Digital (43, 70, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 70, 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]

(70−27, 70, 2564)-Net over F₂₅ — Digital

Digital (43, 70, 2564)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70−27, 70, 6209117)-Net in Base 25 — Upper bound on s

There is no (43, 70, 6209118)-net in base 25, because

1 times m-reduction [i] would yield (43, 69, 6209118)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 2 869859 583883 081442 961025 315462 403545 915748 330278 296249 253727 233796 591105 750615 987287 559609 481745 > 25⁶⁹ [i]