MinT - Best Known (54, 54+53, s)-Nets in Base 8

Best Known (54, 54+53, s)-Nets in Base 8

(54, 54+53, 130)-Net over F₈ — Constructive and digital

Digital (54, 107, 130)-net over F₈, using

1 times m-reduction [i] based on digital (54, 108, 130)-net over F₈, using
- trace code for nets [i] based on digital (0, 54, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]

(54, 54+53, 191)-Net over F₈ — Digital

Digital (54, 107, 191)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+53, 7228)-Net in Base 8 — Upper bound on s

There is no (54, 107, 7229)-net in base 8, because

1 times m-reduction [i] would yield (54, 106, 7229)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 534865 603468 097980 631273 018944 781522 942259 457898 243421 256103 560858 162444 477244 265006 033992 208014 > 8¹⁰⁶ [i]