MinT - Best Known (171−65, 171, s)-Nets in Base 2

Best Known (171−65, 171, s)-Nets in Base 2

(171−65, 171, 66)-Net over F₂ — Constructive and digital

Digital (106, 171, 66)-net over F₂, using

11 times m-reduction [i] based on digital (106, 182, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 91, 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]

(171−65, 171, 91)-Net over F₂ — Digital

Digital (106, 171, 91)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−65, 171, 462)-Net in Base 2 — Upper bound on s

There is no (106, 171, 463)-net in base 2, because

1 times m-reduction [i] would yield (106, 170, 463)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1524 321706 636975 401758 905705 050982 206937 325926 611330 > 2¹⁷⁰ [i]