MinT - Best Known (119, 119+47, s)-Nets in Base 3

Best Known (119, 119+47, s)-Nets in Base 3

(119, 119+47, 252)-Net over F₃ — Constructive and digital

Digital (119, 166, 252)-net over F₃, using

3¹ times duplication [i] based on digital (118, 165, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 55, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(119, 119+47, 459)-Net over F₃ — Digital

Digital (119, 166, 459)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+47, 12458)-Net in Base 3 — Upper bound on s

There is no (119, 166, 12459)-net in base 3, because

1 times m-reduction [i] would yield (119, 165, 12459)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5 312731 565040 973997 417661 392797 087209 138015 085482 110070 778771 255692 911263 560195 > 3¹⁶⁵ [i]