MinT - Best Known (167, 167+85, s)-Nets in Base 2

Best Known (167, 167+85, s)-Nets in Base 2

(167, 167+85, 112)-Net over F₂ — Constructive and digital

Digital (167, 252, 112)-net over F₂, using

t-expansion [i] based on digital (163, 252, 112)-net over F₂, using
- 8 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]

(167, 167+85, 166)-Net over F₂ — Digital

Digital (167, 252, 166)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(167, 167+85, 978)-Net in Base 2 — Upper bound on s

There is no (167, 252, 979)-net in base 2, because

1 times m-reduction [i] would yield (167, 251, 979)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3671 123853 659501 574040 167721 280435 894159 270373 613715 997489 268702 279715 182252 > 2²⁵¹ [i]