MinT - Best Known (85, 85+32, s)-Nets in Base 4

Best Known (85, 85+32, s)-Nets in Base 4

(85, 85+32, 531)-Net over F₄ — Constructive and digital

Digital (85, 117, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 39, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(85, 85+32, 790)-Net over F₄ — Digital

Digital (85, 117, 790)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+32, 57264)-Net in Base 4 — Upper bound on s

There is no (85, 117, 57265)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 27612 494917 686127 578077 744148 147125 645397 885307 588854 493935 966554 203735 > 4¹¹⁷ [i]