MinT - Best Known (64, 64+57, s)-Nets in Base 5

Best Known (64, 64+57, s)-Nets in Base 5

(64, 64+57, 104)-Net over F₅ — Constructive and digital

Digital (64, 121, 104)-net over F₅, using

1 times m-reduction [i] based on digital (64, 122, 104)-net over F₅, using
- trace code for nets [i] based on digital (3, 61, 52)-net over F₂₅, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by GarcÃa and Quoos [i]

(64, 64+57, 149)-Net over F₅ — Digital

Digital (64, 121, 149)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+57, 2775)-Net in Base 5 — Upper bound on s

There is no (64, 121, 2776)-net in base 5, because

1 times m-reduction [i] would yield (64, 120, 2776)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 755997 626914 577072 731037 278167 916382 120982 073724 984458 121658 513384 509215 518413 466625 > 5¹²⁰ [i]