MinT - Best Known (143, 143+57, s)-Nets in Base 3

Best Known (143, 143+57, s)-Nets in Base 3

(143, 143+57, 264)-Net over F₃ — Constructive and digital

Digital (143, 200, 264)-net over F₃, using

1 times m-reduction [i] based on digital (143, 201, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 67, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(143, 143+57, 525)-Net over F₃ — Digital

Digital (143, 200, 525)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(143, 143+57, 13870)-Net in Base 3 — Upper bound on s

There is no (143, 200, 13871)-net in base 3, because

1 times m-reduction [i] would yield (143, 199, 13871)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 88670 928779 515985 495743 358633 795406 090467 792180 969777 340350 185304 161243 881633 782395 554162 894537 > 3¹⁹⁹ [i]