MinT - Best Known (56, 104, s)-Nets in Base 5

Best Known (56, 104, s)-Nets in Base 5

(56, 104, 132)-Net over F₅ — Constructive and digital

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, 104, 141)-Net over F₅ — Digital

Digital (56, 104, 141)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 104, 2601)-Net in Base 5 — Upper bound on s

There is no (56, 104, 2602)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4 940932 542024 783310 140177 200825 431944 270298 251317 091920 827765 318842 615425 > 5¹⁰⁴ [i]