MinT - Best Known (67, 67+23, s)-Nets in Base 2

Best Known (67, 67+23, s)-Nets in Base 2

(67, 67+23, 102)-Net over F₂ — Constructive and digital

Digital (67, 90, 102)-net over F₂, using

trace code for nets [i] based on digital (7, 30, 34)-net over F₈, using
- net from sequence [i] based on digital (7, 33)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
    - a function field by SÃ©mirat [i]

(67, 67+23, 142)-Net over F₂ — Digital

Digital (67, 90, 142)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+23, 1322)-Net in Base 2 — Upper bound on s

There is no (67, 90, 1323)-net in base 2, because

1 times m-reduction [i] would yield (67, 89, 1323)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 621 049379 469986 644163 180734 > 2⁸⁹ [i]