MinT - Best Known (256−91, 256, s)-Nets in Base 2

Best Known (256−91, 256, s)-Nets in Base 2

(256−91, 256, 112)-Net over F₂ — Constructive and digital

Digital (165, 256, 112)-net over F₂, using

t-expansion [i] based on digital (163, 256, 112)-net over F₂, using
- 4 times m-reduction [i] based on digital (163, 260, 112)-net over F₂, using
  - trace code for nets [i] based on digital (33, 130, 56)-net over F₄, using
    - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
        F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(256−91, 256, 149)-Net over F₂ — Digital

Digital (165, 256, 149)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−91, 256, 830)-Net in Base 2 — Upper bound on s

There is no (165, 256, 831)-net in base 2, because

1 times m-reduction [i] would yield (165, 255, 831)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 59095 934894 100964 106332 940066 709388 716962 763152 018150 614807 290717 211060 461500 > 2²⁵⁵ [i]