MinT - Best Known (168−66, 168, s)-Nets in Base 2

Best Known (168−66, 168, s)-Nets in Base 2

(168−66, 168, 66)-Net over F₂ — Constructive and digital

Digital (102, 168, 66)-net over F₂, using

6 times m-reduction [i] based on digital (102, 174, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 87, 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]

(168−66, 168, 83)-Net over F₂ — Digital

Digital (102, 168, 83)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−66, 168, 401)-Net in Base 2 — Upper bound on s

There is no (102, 168, 402)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 376 369077 006936 475486 620174 839990 321014 432940 046740 > 2¹⁶⁸ [i]