MinT - Best Known (180, 180+54, s)-Nets in Base 3

Best Known (180, 180+54, s)-Nets in Base 3

(180, 180+54, 600)-Net over F₃ — Constructive and digital

Digital (180, 234, 600)-net over F₃, using

3² times duplication [i] based on digital (178, 232, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 58, 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]

(180, 180+54, 1342)-Net over F₃ — Digital

Digital (180, 234, 1342)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180, 180+54, 74520)-Net in Base 3 — Upper bound on s

There is no (180, 234, 74521)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4431 183468 964872 953883 247237 997783 360482 368939 035210 669635 442595 399898 906065 378842 287855 641104 918230 840866 605787 > 3²³⁴ [i]