MinT - Best Known (140−42, 140, s)-Nets in Base 3

Best Known (140−42, 140, s)-Nets in Base 3

(140−42, 140, 192)-Net over F₃ — Constructive and digital

Digital (98, 140, 192)-net over F₃, using

1 times m-reduction [i] based on digital (98, 141, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 47, 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]

(140−42, 140, 328)-Net over F₃ — Digital

Digital (98, 140, 328)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−42, 140, 6560)-Net in Base 3 — Upper bound on s

There is no (98, 140, 6561)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 281619 663966 056496 683417 858723 226288 965322 881577 992603 586316 398067 > 3¹⁴⁰ [i]