MinT - Best Known (56, 56+45, s)-Nets in Base 5

Best Known (56, 56+45, s)-Nets in Base 5

(56, 56+45, 132)-Net over F₅ — Constructive and digital

Digital (56, 101, 132)-net over F₅, using

3 times m-reduction [i] based on digital (56, 104, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 52, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(56, 56+45, 157)-Net over F₅ — Digital

Digital (56, 101, 157)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+45, 3387)-Net in Base 5 — Upper bound on s

There is no (56, 101, 3388)-net in base 5, because

1 times m-reduction [i] would yield (56, 100, 3388)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7911 291792 365457 010749 194915 477633 875284 581886 403525 611083 811403 356225 > 5¹⁰⁰ [i]