MinT - Best Known (166, 166+81, s)-Nets in Base 2

Best Known (166, 166+81, s)-Nets in Base 2

(166, 166+81, 112)-Net over F₂ — Constructive and digital

Digital (166, 247, 112)-net over F₂, using

t-expansion [i] based on digital (163, 247, 112)-net over F₂, using
- 13 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]

(166, 166+81, 174)-Net over F₂ — Digital

Digital (166, 247, 174)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(166, 166+81, 1061)-Net in Base 2 — Upper bound on s

There is no (166, 247, 1062)-net in base 2, because

1 times m-reduction [i] would yield (166, 246, 1062)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 114 422688 051200 388545 266526 873117 076716 528017 399059 759002 162674 669233 653152 > 2²⁴⁶ [i]