MinT - Best Known (58, 58+50, s)-Nets in Base 5

Best Known (58, 58+50, s)-Nets in Base 5

(58, 58+50, 132)-Net over F₅ — Constructive and digital

Digital (58, 108, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 54, 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]

(58, 58+50, 144)-Net over F₅ — Digital

Digital (58, 108, 144)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+50, 2643)-Net in Base 5 — Upper bound on s

There is no (58, 108, 2644)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3103 788827 901760 266180 031342 779362 458880 548186 013693 056711 140897 886689 649745 > 5¹⁰⁸ [i]