MinT - Best Known (143, 143+69, s)-Nets in Base 2

Best Known (143, 143+69, s)-Nets in Base 2

(143, 143+69, 112)-Net over F₂ — Constructive and digital

Digital (143, 212, 112)-net over F₂, using

8 times m-reduction [i] based on digital (143, 220, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 110, 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]

(143, 143+69, 155)-Net over F₂ — Digital

Digital (143, 212, 155)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(143, 143+69, 949)-Net in Base 2 — Upper bound on s

There is no (143, 212, 950)-net in base 2, because

1 times m-reduction [i] would yield (143, 211, 950)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3314 602394 761250 650240 579070 102776 410632 588398 055098 664504 718654 > 2²¹¹ [i]