MinT - Best Known (232−68, 232, s)-Nets in Base 2

Best Known (232−68, 232, s)-Nets in Base 2

(232−68, 232, 135)-Net over F₂ — Constructive and digital

Digital (164, 232, 135)-net over F₂, using

2¹ times duplication [i] based on digital (163, 231, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 77, 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]

(232−68, 232, 214)-Net over F₂ — Digital

Digital (164, 232, 214)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−68, 232, 1483)-Net in Base 2 — Upper bound on s

There is no (164, 232, 1484)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7006 624132 180736 161749 325777 166389 215368 912516 411002 787621 110175 730366 > 2²³² [i]