MinT - Best Known (141−51, 141, s)-Nets in Base 2

Best Known (141−51, 141, s)-Nets in Base 2

(141−51, 141, 66)-Net over F₂ — Constructive and digital

Digital (90, 141, 66)-net over F₂, using

9 times m-reduction [i] based on digital (90, 150, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 75, 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]

(141−51, 141, 87)-Net over F₂ — Digital

Digital (90, 141, 87)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−51, 141, 457)-Net in Base 2 — Upper bound on s

There is no (90, 141, 458)-net in base 2, because

1 times m-reduction [i] would yield (90, 140, 458)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 405403 316023 112617 854835 193841 915988 118420 > 2¹⁴⁰ [i]