MinT - Best Known (169−65, 169, s)-Nets in Base 2

Best Known (169−65, 169, s)-Nets in Base 2

(169−65, 169, 66)-Net over F₂ — Constructive and digital

Digital (104, 169, 66)-net over F₂, using

9 times m-reduction [i] based on digital (104, 178, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 89, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(169−65, 169, 88)-Net over F₂ — Digital

Digital (104, 169, 88)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−65, 169, 441)-Net in Base 2 — Upper bound on s

There is no (104, 169, 442)-net in base 2, because

1 times m-reduction [i] would yield (104, 168, 442)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 393 353667 283779 744514 756895 637963 188719 491402 477015 > 2¹⁶⁸ [i]