MinT - Best Known (142, 142+65, s)-Nets in Base 2

Best Known (142, 142+65, s)-Nets in Base 2

(142, 142+65, 112)-Net over F₂ — Constructive and digital

Digital (142, 207, 112)-net over F₂, using

11 times m-reduction [i] based on digital (142, 218, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 109, 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]

(142, 142+65, 165)-Net over F₂ — Digital

Digital (142, 207, 165)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 142+65, 1061)-Net in Base 2 — Upper bound on s

There is no (142, 207, 1062)-net in base 2, because

1 times m-reduction [i] would yield (142, 206, 1062)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 102 919592 212562 516474 125980 082896 609192 902631 420618 189319 625753 > 2²⁰⁶ [i]