MinT - Best Known (86−40, 86, s)-Nets in Base 3

Best Known (86−40, 86, s)-Nets in Base 3

(86−40, 86, 56)-Net over F₃ — Constructive and digital

Digital (46, 86, 56)-net over F₃, using

trace code for nets [i] based on digital (3, 43, 28)-net over F₉, using
- net from sequence [i] based on digital (3, 27)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
    - the Hermitian function field over F₉ [i]

(86−40, 86, 62)-Net over F₃ — Digital

Digital (46, 86, 62)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(86−40, 86, 448)-Net in Base 3 — Upper bound on s

There is no (46, 86, 449)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 110281 532418 431206 814239 573370 747506 862481 > 3⁸⁶ [i]