MinT - Best Known (53, 53+47, s)-Nets in Base 8

Best Known (53, 53+47, s)-Nets in Base 8

(53, 53+47, 208)-Net over F₈ — Constructive and digital

Digital (53, 100, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 50, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(53, 53+47, 226)-Net over F₈ — Digital

Digital (53, 100, 226)-net over F₈, using

trace code for nets [i] based on digital (3, 50, 113)-net over F₆₄, using
- net from sequence [i] based on digital (3, 112)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 113, using
    - a curve from the manYPoints database [i]

(53, 53+47, 10374)-Net in Base 8 — Upper bound on s

There is no (53, 100, 10375)-net in base 8, because

1 times m-reduction [i] would yield (53, 99, 10375)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 254815 302045 791842 362926 159498 096940 778985 243109 345150 492150 592410 889887 688351 978618 710976 > 8⁹⁹ [i]