MinT - Best Known (134−35, 134, s)-Nets in Base 3

Best Known (134−35, 134, s)-Nets in Base 3

(134−35, 134, 264)-Net over F₃ — Constructive and digital

Digital (99, 134, 264)-net over F₃, using

1 times m-reduction [i] based on digital (99, 135, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 45, 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]

(134−35, 134, 523)-Net over F₃ — Digital

Digital (99, 134, 523)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−35, 134, 19378)-Net in Base 3 — Upper bound on s

There is no (99, 134, 19379)-net in base 3, because

1 times m-reduction [i] would yield (99, 133, 19379)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2866 525648 242432 459964 346137 553074 993863 761147 769391 210327 620039 > 3¹³³ [i]