MinT - Best Known (142−55, 142, s)-Nets in Base 2

Best Known (142−55, 142, s)-Nets in Base 2

(142−55, 142, 66)-Net over F₂ — Constructive and digital

Digital (87, 142, 66)-net over F₂, using

2 times m-reduction [i] based on digital (87, 144, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 72, 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]

(142−55, 142, 75)-Net over F₂ — Digital

Digital (87, 142, 75)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−55, 142, 369)-Net in Base 2 — Upper bound on s

There is no (87, 142, 370)-net in base 2, because

1 times m-reduction [i] would yield (87, 141, 370)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 880914 416248 048749 326279 445240 589952 688736 > 2¹⁴¹ [i]