MinT - Best Known (208−86, 208, s)-Nets in Base 2

Best Known (208−86, 208, s)-Nets in Base 2

(208−86, 208, 66)-Net over F₂ — Constructive and digital

Digital (122, 208, 66)-net over F₂, using

6 times m-reduction [i] based on digital (122, 214, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 107, 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]

(208−86, 208, 88)-Net over F₂ — Digital

Digital (122, 208, 88)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−86, 208, 422)-Net in Base 2 — Upper bound on s

There is no (122, 208, 423)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 439 979685 437345 385173 168404 343646 409292 287644 999925 117488 866784 > 2²⁰⁸ [i]