MinT - Best Known (165, 165+65, s)-Nets in Base 2

Best Known (165, 165+65, s)-Nets in Base 2

(165, 165+65, 144)-Net over F₂ — Constructive and digital

Digital (165, 230, 144)-net over F₂, using

1 times m-reduction [i] based on digital (165, 231, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 77, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(165, 165+65, 232)-Net over F₂ — Digital

Digital (165, 230, 232)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(165, 165+65, 1777)-Net in Base 2 — Upper bound on s

There is no (165, 230, 1778)-net in base 2, because

1 times m-reduction [i] would yield (165, 229, 1778)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 870 555840 688036 802404 012230 408625 986416 911800 193772 325784 252839 067773 > 2²²⁹ [i]