MinT - Best Known (134−35, 134, s)-Nets in Base 2

Best Known (134−35, 134, s)-Nets in Base 2

(134−35, 134, 135)-Net over F₂ — Constructive and digital

Digital (99, 134, 135)-net over F₂, using

1 times m-reduction [i] based on digital (99, 135, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 45, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(134−35, 134, 182)-Net over F₂ — Digital

Digital (99, 134, 182)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−35, 134, 1600)-Net in Base 2 — Upper bound on s

There is no (99, 134, 1601)-net in base 2, because

1 times m-reduction [i] would yield (99, 133, 1601)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10894 176306 387477 892028 753741 759431 479352 > 2¹³³ [i]