MinT - Best Known (80−37, 80, s)-Nets in Base 8

Best Known (80−37, 80, s)-Nets in Base 8

(80−37, 80, 208)-Net over F₈ — Constructive and digital

Digital (43, 80, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 40, 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]

(80−37, 80, 226)-Net over F₈ — Digital

Digital (43, 80, 226)-net over F₈, using

trace code for nets [i] based on digital (3, 40, 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]

(80−37, 80, 9910)-Net in Base 8 — Upper bound on s

There is no (43, 80, 9911)-net in base 8, because

1 times m-reduction [i] would yield (43, 79, 9911)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 220934 192744 524096 975763 577695 644662 481709 734998 294854 589522 470694 492517 > 8⁷⁹ [i]