MinT - Best Known (54, 54+46, s)-Nets in Base 5

Best Known (54, 54+46, s)-Nets in Base 5

(54, 54+46, 132)-Net over F₅ — Constructive and digital

Digital (54, 100, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 50, 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]

(54, 54+46, 138)-Net over F₅ — Digital

Digital (54, 100, 138)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+46, 2561)-Net in Base 5 — Upper bound on s

There is no (54, 100, 2562)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7891 264272 149711 667416 454084 946889 793383 837169 431553 711222 980341 456425 > 5¹⁰⁰ [i]