MinT - Best Known (46, 46+20, s)-Nets in Base 3

Best Known (46, 46+20, s)-Nets in Base 3

(46, 46+20, 144)-Net over F₃ — Constructive and digital

Digital (46, 66, 144)-net over F₃, using

trace code for nets [i] based on digital (2, 22, 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]

(46, 46+20, 186)-Net over F₃ — Digital

Digital (46, 66, 186)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 46+20, 3181)-Net in Base 3 — Upper bound on s

There is no (46, 66, 3182)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 30 936365 226436 948886 455859 190701 > 3⁶⁶ [i]