MinT - Best Known (185−53, 185, s)-Nets in Base 3

Best Known (185−53, 185, s)-Nets in Base 3

(185−53, 185, 252)-Net over F₃ — Constructive and digital

Digital (132, 185, 252)-net over F₃, using

1 times m-reduction [i] based on digital (132, 186, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 62, 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]

(185−53, 185, 483)-Net over F₃ — Digital

Digital (132, 185, 483)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−53, 185, 12529)-Net in Base 3 — Upper bound on s

There is no (132, 185, 12530)-net in base 3, because

1 times m-reduction [i] would yield (132, 184, 12530)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6177 684580 859422 281563 143684 086126 495882 222530 642760 364185 387908 445870 617572 015759 705125 > 3¹⁸⁴ [i]