MinT - Best Known (162, 162+73, s)-Nets in Base 2

Best Known (162, 162+73, s)-Nets in Base 2

(162, 162+73, 112)-Net over F₂ — Constructive and digital

Digital (162, 235, 112)-net over F₂, using

23 times m-reduction [i] based on digital (162, 258, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 129, 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]

(162, 162+73, 188)-Net over F₂ — Digital

Digital (162, 235, 188)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 162+73, 1239)-Net in Base 2 — Upper bound on s

There is no (162, 235, 1240)-net in base 2, because

1 times m-reduction [i] would yield (162, 234, 1240)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 27609 699354 228737 927441 046661 019084 891449 031912 680309 337136 719675 048858 > 2²³⁴ [i]