MinT - Best Known (78−26, 78, s)-Nets in Base 4

Best Known (78−26, 78, s)-Nets in Base 4

(78−26, 78, 195)-Net over F₄ — Constructive and digital

Digital (52, 78, 195)-net over F₄, using

trace code for nets [i] based on digital (0, 26, 65)-net over F₆₄, using
- net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
    - the rational function field F₆₄(x) [i]
  - Niederreiter sequence [i]

(78−26, 78, 263)-Net over F₄ — Digital

Digital (52, 78, 263)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(78−26, 78, 7727)-Net in Base 4 — Upper bound on s

There is no (52, 78, 7728)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 91350 031566 248770 185206 110977 208489 515303 385795 > 4⁷⁸ [i]