MinT - Best Known (78−24, 78, s)-Nets in Base 3

Best Known (78−24, 78, s)-Nets in Base 3

(78−24, 78, 144)-Net over F₃ — Constructive and digital

Digital (54, 78, 144)-net over F₃, using

trace code for nets [i] based on digital (2, 26, 48)-net over F₂₇, using
- net from sequence [i] based on digital (2, 47)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 2 and N(F) ≥ 48, using
    - a function field by GarcÃa and Quoos [i]

(78−24, 78, 195)-Net over F₃ — Digital

Digital (54, 78, 195)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(78−24, 78, 3327)-Net in Base 3 — Upper bound on s

There is no (54, 78, 3328)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16 450325 180491 529563 330473 065881 106433 > 3⁷⁸ [i]