MinT - Best Known (144, 144+44, s)-Nets in Base 3

Best Known (144, 144+44, s)-Nets in Base 3

(144, 144+44, 464)-Net over F₃ — Constructive and digital

Digital (144, 188, 464)-net over F₃, using

t-expansion [i] based on digital (143, 188, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 47, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(144, 144+44, 1050)-Net over F₃ — Digital

Digital (144, 188, 1050)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 144+44, 54059)-Net in Base 3 — Upper bound on s

There is no (144, 188, 54060)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 499993 905921 945487 836371 598906 505856 424571 962378 107620 234019 154675 257734 110792 291064 705737 > 3¹⁸⁸ [i]