MinT - Best Known (168, 168+73, s)-Nets in Base 3

Best Known (168, 168+73, s)-Nets in Base 3

(168, 168+73, 246)-Net over F₃ — Constructive and digital

Digital (168, 241, 246)-net over F₃, using

3¹ times duplication [i] based on digital (167, 240, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 80, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(168, 168+73, 506)-Net over F₃ — Digital

Digital (168, 241, 506)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(168, 168+73, 10791)-Net in Base 3 — Upper bound on s

There is no (168, 241, 10792)-net in base 3, because

1 times m-reduction [i] would yield (168, 240, 10792)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 232135 378738 535641 491725 295622 205847 314419 307778 672616 128478 829740 653335 002136 960796 444130 167685 087994 869907 791425 > 3²⁴⁰ [i]