MinT - Best Known (119, 172, s)-Nets in Base 3

Best Known (119, 172, s)-Nets in Base 3

(119, 172, 192)-Net over F₃ — Constructive and digital

Digital (119, 172, 192)-net over F₃, using

3¹ times duplication [i] based on digital (118, 171, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 57, 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]

(119, 172, 357)-Net over F₃ — Digital

Digital (119, 172, 357)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 172, 7223)-Net in Base 3 — Upper bound on s

There is no (119, 172, 7224)-net in base 3, because

1 times m-reduction [i] would yield (119, 171, 7224)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3882 504529 641962 520729 202819 209816 950352 267093 101336 048451 511691 293888 141029 938001 > 3¹⁷¹ [i]