MinT - Best Known (109, 186, s)-Nets in Base 2

Best Known (109, 186, s)-Nets in Base 2

(109, 186, 66)-Net over F₂ — Constructive and digital

Digital (109, 186, 66)-net over F₂, using

2 times m-reduction [i] based on digital (109, 188, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 94, 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]

(109, 186, 80)-Net over F₂ — Digital

Digital (109, 186, 80)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 186, 385)-Net in Base 2 — Upper bound on s

There is no (109, 186, 386)-net in base 2, because

1 times m-reduction [i] would yield (109, 185, 386)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 51 286049 937250 054207 932272 581943 233310 640468 104527 928128 > 2¹⁸⁵ [i]