MinT - Best Known (207−86, 207, s)-Nets in Base 2

Best Known (207−86, 207, s)-Nets in Base 2

(207−86, 207, 66)-Net over F₂ — Constructive and digital

Digital (121, 207, 66)-net over F₂, using

5 times m-reduction [i] based on digital (121, 212, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 106, 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]

(207−86, 207, 87)-Net over F₂ — Digital

Digital (121, 207, 87)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−86, 207, 414)-Net in Base 2 — Upper bound on s

There is no (121, 207, 415)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 213 570394 391268 101861 998031 956790 136214 437595 492542 318772 963944 > 2²⁰⁷ [i]