MinT - Best Known (146−57, 146, s)-Nets in Base 2

Best Known (146−57, 146, s)-Nets in Base 2

(146−57, 146, 66)-Net over F₂ — Constructive and digital

Digital (89, 146, 66)-net over F₂, using

2 times m-reduction [i] based on digital (89, 148, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 74, 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]

(146−57, 146, 75)-Net over F₂ — Digital

Digital (89, 146, 75)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−57, 146, 369)-Net in Base 2 — Upper bound on s

There is no (89, 146, 370)-net in base 2, because

1 times m-reduction [i] would yield (89, 145, 370)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 46 169798 785601 331784 922022 611030 711596 313016 > 2¹⁴⁵ [i]