MinT - Best Known (182−40, 182, s)-Nets in Base 3

Best Known (182−40, 182, s)-Nets in Base 3

(182−40, 182, 640)-Net over F₃ — Constructive and digital

Digital (142, 182, 640)-net over F₃, using

3² times duplication [i] based on 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]

(182−40, 182, 1316)-Net over F₃ — Digital

Digital (142, 182, 1316)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−40, 182, 91198)-Net in Base 3 — Upper bound on s

There is no (142, 182, 91199)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 685 699224 877552 067808 136360 346962 989686 526088 677113 759292 771577 386992 641736 637365 022681 > 3¹⁸² [i]