MinT - Best Known (140, 140+63, s)-Nets in Base 3

Best Known (140, 140+63, s)-Nets in Base 3

(140, 140+63, 192)-Net over F₃ — Constructive and digital

Digital (140, 203, 192)-net over F₃, using

1 times m-reduction [i] based on digital (140, 204, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 68, 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, 140+63, 403)-Net over F₃ — Digital

Digital (140, 203, 403)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(140, 140+63, 7949)-Net in Base 3 — Upper bound on s

There is no (140, 203, 7950)-net in base 3, because

1 times m-reduction [i] would yield (140, 202, 7950)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 397503 532761 977109 014878 600466 984754 506332 342444 238474 602980 030825 591207 839619 328760 058547 293577 > 3²⁰² [i]