MinT - Best Known (180−40, 180, s)-Nets in Base 3

Best Known (180−40, 180, s)-Nets in Base 3

(180−40, 180, 640)-Net over F₃ — Constructive and digital

Digital (140, 180, 640)-net over F₃, using

trace code for nets [i] based on digital (5, 45, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(180−40, 180, 1245)-Net over F₃ — Digital

Digital (140, 180, 1245)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−40, 180, 81707)-Net in Base 3 — Upper bound on s

There is no (140, 180, 81708)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 76 179720 562726 182063 491230 264661 682921 992911 435493 400933 761727 448281 925771 060253 286657 > 3¹⁸⁰ [i]