MinT - Best Known (86, 86+45, s)-Nets in Base 2

Best Known (86, 86+45, s)-Nets in Base 2

(86, 86+45, 66)-Net over F₂ — Constructive and digital

Digital (86, 131, 66)-net over F₂, using

11 times m-reduction [i] based on digital (86, 142, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 71, 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]

(86, 86+45, 92)-Net over F₂ — Digital

Digital (86, 131, 92)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+45, 512)-Net in Base 2 — Upper bound on s

There is no (86, 131, 513)-net in base 2, because

1 times m-reduction [i] would yield (86, 130, 513)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1392 250576 663000 496546 555994 545074 546432 > 2¹³⁰ [i]