MinT - Best Known (116−53, 116, s)-Nets in Base 3

Best Known (116−53, 116, s)-Nets in Base 3

(116−53, 116, 64)-Net over F₃ — Constructive and digital

Digital (63, 116, 64)-net over F₃, using

trace code for nets [i] based on digital (5, 58, 32)-net over F₉, using
- net from sequence [i] based on digital (5, 31)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
    - a function field by GarcÃa and Quoos [i]

(116−53, 116, 82)-Net over F₃ — Digital

Digital (63, 116, 82)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−53, 116, 655)-Net in Base 3 — Upper bound on s

There is no (63, 116, 656)-net in base 3, because

1 times m-reduction [i] would yield (63, 115, 656)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 669943 341877 683393 360777 525398 074493 568553 197248 370785 > 3¹¹⁵ [i]