MinT - Best Known (169−45, 169, s)-Nets in Base 2

Best Known (169−45, 169, s)-Nets in Base 2

(169−45, 169, 144)-Net over F₂ — Constructive and digital

Digital (124, 169, 144)-net over F₂, using

2¹ times duplication [i] based on digital (123, 168, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 56, 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]

(169−45, 169, 207)-Net over F₂ — Digital

Digital (124, 169, 207)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−45, 169, 1769)-Net in Base 2 — Upper bound on s

There is no (124, 169, 1770)-net in base 2, because

1 times m-reduction [i] would yield (124, 168, 1770)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 377 647074 562085 550818 844102 131851 448244 241953 279912 > 2¹⁶⁸ [i]