MinT - Best Known (164, 164+65, s)-Nets in Base 2

Best Known (164, 164+65, s)-Nets in Base 2

(164, 164+65, 144)-Net over F₂ — Constructive and digital

Digital (164, 229, 144)-net over F₂, using

2¹ times duplication [i] based on digital (163, 228, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 76, 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]

(164, 164+65, 229)-Net over F₂ — Digital

Digital (164, 229, 229)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(164, 164+65, 1738)-Net in Base 2 — Upper bound on s

There is no (164, 229, 1739)-net in base 2, because

1 times m-reduction [i] would yield (164, 228, 1739)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 436 001797 163012 961403 031059 833898 480042 340503 284575 946794 709266 363946 > 2²²⁸ [i]