MinT - Best Known (165, 165+90, s)-Nets in Base 2

Best Known (165, 165+90, s)-Nets in Base 2

(165, 165+90, 112)-Net over F₂ — Constructive and digital

Digital (165, 255, 112)-net over F₂, using

t-expansion [i] based on digital (163, 255, 112)-net over F₂, using
- 5 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]

(165, 165+90, 151)-Net over F₂ — Digital

Digital (165, 255, 151)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(165, 165+90, 830)-Net in Base 2 — Upper bound on s

There is no (165, 255, 831)-net in base 2, because

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]