MinT - Best Known (142−37, 142, s)-Nets in Base 3

Best Known (142−37, 142, s)-Nets in Base 3

(142−37, 142, 282)-Net over F₃ — Constructive and digital

Digital (105, 142, 282)-net over F₃, using

3¹ times duplication [i] based on digital (104, 141, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 47, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(142−37, 142, 552)-Net over F₃ — Digital

Digital (105, 142, 552)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−37, 142, 20614)-Net in Base 3 — Upper bound on s

There is no (105, 142, 20615)-net in base 3, because

1 times m-reduction [i] would yield (105, 141, 20615)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 798790 868750 656015 192155 762506 007150 405409 535722 700845 159097 906541 > 3¹⁴¹ [i]