MinT - Best Known (138, 208, s)-Nets in Base 2

Best Known (138, 208, s)-Nets in Base 2

(138, 208, 112)-Net over F₂ — Constructive and digital

Digital (138, 208, 112)-net over F₂, using

2 times m-reduction [i] based on digital (138, 210, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 105, 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]

(138, 208, 141)-Net over F₂ — Digital

Digital (138, 208, 141)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 208, 804)-Net in Base 2 — Upper bound on s

There is no (138, 208, 805)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 412 331386 069400 302059 072555 937886 762150 383764 015138 604420 736096 > 2²⁰⁸ [i]