MinT - Best Known (144, 212, s)-Nets in Base 2

Best Known (144, 212, s)-Nets in Base 2

(144, 212, 112)-Net over F₂ — Constructive and digital

Digital (144, 212, 112)-net over F₂, using

10 times m-reduction [i] based on digital (144, 222, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 111, 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]

(144, 212, 160)-Net over F₂ — Digital

Digital (144, 212, 160)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 212, 970)-Net in Base 2 — Upper bound on s

There is no (144, 212, 971)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6727 125403 702292 605111 794275 476103 667557 900567 815998 238042 629330 > 2²¹² [i]