MinT - Best Known (191−75, 191, s)-Nets in Base 2

Best Known (191−75, 191, s)-Nets in Base 2

(191−75, 191, 66)-Net over F₂ — Constructive and digital

Digital (116, 191, 66)-net over F₂, using

11 times m-reduction [i] based on digital (116, 202, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 101, 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]

(191−75, 191, 93)-Net over F₂ — Digital

Digital (116, 191, 93)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(191−75, 191, 462)-Net in Base 2 — Upper bound on s

There is no (116, 191, 463)-net in base 2, because

1 times m-reduction [i] would yield (116, 190, 463)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1631 540427 442346 921344 790515 223862 817331 688817 189566 170680 > 2¹⁹⁰ [i]