MinT - Best Known (140−39, 140, s)-Nets in Base 3

Best Known (140−39, 140, s)-Nets in Base 3

(140−39, 140, 246)-Net over F₃ — Constructive and digital

Digital (101, 140, 246)-net over F₃, using

1 times m-reduction [i] based on digital (101, 141, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 47, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(140−39, 140, 424)-Net over F₃ — Digital

Digital (101, 140, 424)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−39, 140, 12247)-Net in Base 3 — Upper bound on s

There is no (101, 140, 12248)-net in base 3, because

1 times m-reduction [i] would yield (101, 139, 12248)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 090066 225733 845605 713088 561842 533466 431688 835978 136223 950340 855009 > 3¹³⁹ [i]