MinT - Best Known (143−43, 143, s)-Nets in Base 3

Best Known (143−43, 143, s)-Nets in Base 3

(143−43, 143, 192)-Net over F₃ — Constructive and digital

Digital (100, 143, 192)-net over F₃, using

1 times m-reduction [i] based on digital (100, 144, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 48, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(143−43, 143, 331)-Net over F₃ — Digital

Digital (100, 143, 331)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−43, 143, 7286)-Net in Base 3 — Upper bound on s

There is no (100, 143, 7287)-net in base 3, because

1 times m-reduction [i] would yield (100, 142, 7287)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 56 545925 607977 014598 868773 254472 442227 862092 041544 112659 755558 250375 > 3¹⁴² [i]