MinT - Best Known (132−38, 132, s)-Nets in Base 3

Best Known (132−38, 132, s)-Nets in Base 3

(132−38, 132, 228)-Net over F₃ — Constructive and digital

Digital (94, 132, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 44, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(132−38, 132, 361)-Net over F₃ — Digital

Digital (94, 132, 361)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−38, 132, 8164)-Net in Base 3 — Upper bound on s

There is no (94, 132, 8165)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 955 653194 899060 862210 460321 076234 052635 190495 009410 515366 355371 > 3¹³² [i]