MinT - Best Known (214−62, 214, s)-Nets in Base 2

Best Known (214−62, 214, s)-Nets in Base 2

(214−62, 214, 135)-Net over F₂ — Constructive and digital

Digital (152, 214, 135)-net over F₂, using

2¹ times duplication [i] based on digital (151, 213, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 71, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(214−62, 214, 206)-Net over F₂ — Digital

Digital (152, 214, 206)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−62, 214, 1440)-Net in Base 2 — Upper bound on s

There is no (152, 214, 1441)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 26352 123518 260832 022047 129455 359113 597205 049929 120819 217212 620800 > 2²¹⁴ [i]