MinT - Best Known (143, 143+42, s)-Nets in Base 3

Best Known (143, 143+42, s)-Nets in Base 3

(143, 143+42, 600)-Net over F₃ — Constructive and digital

Digital (143, 185, 600)-net over F₃, using

3¹ times duplication [i] based on digital (142, 184, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 46, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(143, 143+42, 1168)-Net over F₃ — Digital

Digital (143, 185, 1168)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(143, 143+42, 69269)-Net in Base 3 — Upper bound on s

There is no (143, 185, 69270)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18511 144152 882027 421531 126376 323588 010291 962906 740210 819297 041205 058677 542455 573163 633253 > 3¹⁸⁵ [i]