MinT - Best Known (142, 142+45, s)-Nets in Base 3

Best Known (142, 142+45, s)-Nets in Base 3

(142, 142+45, 400)-Net over F₃ — Constructive and digital

Digital (142, 187, 400)-net over F₃, using

1 times m-reduction [i] based on digital (142, 188, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 47, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(142, 142+45, 940)-Net over F₃ — Digital

Digital (142, 187, 940)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 142+45, 48918)-Net in Base 3 — Upper bound on s

There is no (142, 187, 48919)-net in base 3, because

1 times m-reduction [i] would yield (142, 186, 48919)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 55538 914213 391726 059678 478512 502838 786861 160707 706196 399171 863053 445964 014557 650245 930821 > 3¹⁸⁶ [i]