MinT - Best Known (7, 25, s)-Nets in Base 64

Best Known (7, 25, s)-Nets in Base 64

(7, 25, 177)-Net over F₆₄ — Constructive and digital

Digital (7, 25, 177)-net over F₆₄, using

net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
  - a function field by GarcÃa and Quoos [i]

(7, 25, 257)-Net in Base 64 — Constructive

(7, 25, 257)-net in base 64, using

3 times m-reduction [i] based on (7, 28, 257)-net in base 64, using
- base change [i] based on digital (0, 21, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(7, 25, 6844)-Net in Base 64 — Upper bound on s

There is no (7, 25, 6845)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 1428 984796 468234 329362 207542 653392 802543 105148 > 64²⁵ [i]