MinT - Best Known (143−68, 143, s)-Nets in Base 3

Best Known (143−68, 143, s)-Nets in Base 3

(143−68, 143, 64)-Net over F₃ — Constructive and digital

Digital (75, 143, 64)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (15, 49, 28)-net over F₃, using
  - net from sequence [i] based on digital (15, 27)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
      - an explicitly constructive algebraic function field [i]
2. digital (26, 94, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using
      - an explicitly constructive algebraic function field [i]

(143−68, 143, 87)-Net over F₃ — Digital

Digital (75, 143, 87)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−68, 143, 654)-Net in Base 3 — Upper bound on s

There is no (75, 143, 655)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 173 520827 375920 588091 887802 194302 901500 324385 993809 473701 208438 501085 > 3¹⁴³ [i]