MinT - Best Known (142−51, 142, s)-Nets in Base 2

Best Known (142−51, 142, s)-Nets in Base 2

(142−51, 142, 66)-Net over F₂ — Constructive and digital

Digital (91, 142, 66)-net over F₂, using

10 times m-reduction [i] based on digital (91, 152, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 76, 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]

(142−51, 142, 89)-Net over F₂ — Digital

Digital (91, 142, 89)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−51, 142, 471)-Net in Base 2 — Upper bound on s

There is no (91, 142, 472)-net in base 2, because

1 times m-reduction [i] would yield (91, 141, 472)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 831652 217842 542950 731826 679396 493660 814520 > 2¹⁴¹ [i]