MinT - Best Known (142, 218, s)-Nets in Base 2

Best Known (142, 218, s)-Nets in Base 2

(142, 218, 112)-Net over F₂ — Constructive and digital

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, 218, 136)-Net over F₂ — Digital

Digital (142, 218, 136)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 218, 746)-Net in Base 2 — Upper bound on s

There is no (142, 218, 747)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 431374 270707 794873 763400 642837 062171 835682 528655 143961 597012 577110 > 2²¹⁸ [i]