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

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

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

Digital (53, 106, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 53, 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]

(53, 53+53, 183)-Net over F₈ — Digital

Digital (53, 106, 183)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+53, 6671)-Net in Base 8 — Upper bound on s

There is no (53, 106, 6672)-net in base 8, because

1 times m-reduction [i] would yield (53, 105, 6672)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 66830 421185 558629 634619 875642 451572 858684 879217 333073 790990 943813 746800 480590 191961 247443 215200 > 8¹⁰⁵ [i]