MinT - Best Known (146−53, 146, s)-Nets in Base 2

Best Known (146−53, 146, s)-Nets in Base 2

(146−53, 146, 66)-Net over F₂ — Constructive and digital

Digital (93, 146, 66)-net over F₂, using

10 times m-reduction [i] based on digital (93, 156, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 78, 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]

(146−53, 146, 89)-Net over F₂ — Digital

Digital (93, 146, 89)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−53, 146, 466)-Net in Base 2 — Upper bound on s

There is no (93, 146, 467)-net in base 2, because

1 times m-reduction [i] would yield (93, 145, 467)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 45 954405 281900 727190 848259 435593 227056 230680 > 2¹⁴⁵ [i]