MinT - Best Known (180, 180+55, s)-Nets in Base 3

Best Known (180, 180+55, s)-Nets in Base 3

(180, 180+55, 464)-Net over F₃ — Constructive and digital

Digital (180, 235, 464)-net over F₃, using

t-expansion [i] based on digital (179, 235, 464)-net over F₃, using
- 1 times m-reduction [i] based on digital (179, 236, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 59, 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]

(180, 180+55, 1269)-Net over F₃ — Digital

Digital (180, 235, 1269)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180, 180+55, 74520)-Net in Base 3 — Upper bound on s

There is no (180, 235, 74521)-net in base 3, because

1 times m-reduction [i] would yield (180, 234, 74521)-net in base 3, but
- 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]