MinT - Best Known (222−70, 222, s)-Nets in Base 2

Best Known (222−70, 222, s)-Nets in Base 2

(222−70, 222, 112)-Net over F₂ — Constructive and digital

Digital (152, 222, 112)-net over F₂, using

16 times m-reduction [i] based on digital (152, 238, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 119, 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]

(222−70, 222, 173)-Net over F₂ — Digital

Digital (152, 222, 173)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−70, 222, 1077)-Net in Base 2 — Upper bound on s

There is no (152, 222, 1078)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 747069 032563 232487 790692 235657 545293 730498 770619 922644 987902 403950 > 2²²² [i]