MinT - Best Known (112, 157, s)-Nets in Base 2

Best Known (112, 157, s)-Nets in Base 2

(112, 157, 112)-Net over F₂ — Constructive and digital

Digital (112, 157, 112)-net over F₂, using

1 times m-reduction [i] based on digital (112, 158, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 79, 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]

(112, 157, 163)-Net over F₂ — Digital

Digital (112, 157, 163)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 157, 1202)-Net in Base 2 — Upper bound on s

There is no (112, 157, 1203)-net in base 2, because

1 times m-reduction [i] would yield (112, 156, 1203)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 92640 401852 554805 499530 535582 210395 835948 918888 > 2¹⁵⁶ [i]