MinT - Best Known (116−29, 116, s)-Nets in Base 2

Best Known (116−29, 116, s)-Nets in Base 2

(116−29, 116, 135)-Net over F₂ — Constructive and digital

Digital (87, 116, 135)-net over F₂, using

1 times m-reduction [i] based on digital (87, 117, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 39, 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]

(116−29, 116, 181)-Net over F₂ — Digital

Digital (87, 116, 181)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−29, 116, 1775)-Net in Base 2 — Upper bound on s

There is no (87, 116, 1776)-net in base 2, because

1 times m-reduction [i] would yield (87, 115, 1776)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 41803 900779 615707 381755 935989 741939 > 2¹¹⁵ [i]