MinT - Best Known (127, 127+89, s)-Nets in Base 2

Best Known (127, 127+89, s)-Nets in Base 2

(127, 127+89, 66)-Net over F₂ — Constructive and digital

Digital (127, 216, 66)-net over F₂, using

8 times m-reduction [i] based on digital (127, 224, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 112, 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]

(127, 127+89, 92)-Net over F₂ — Digital

Digital (127, 216, 92)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+89, 448)-Net in Base 2 — Upper bound on s

There is no (127, 216, 449)-net in base 2, because

1 times m-reduction [i] would yield (127, 215, 449)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 55271 962756 137963 744363 279486 286523 010974 124886 410510 834397 547088 > 2²¹⁵ [i]