MinT - Best Known (34−22, 34, s)-Nets in Base 2

Best Known (34−22, 34, s)-Nets in Base 2

(34−22, 34, 14)-Net over F₂ — Constructive and digital

Digital (12, 34, 14)-net over F₂, using

t-expansion [i] based on digital (11, 34, 14)-net over F₂, using
- net from sequence [i] based on digital (11, 13)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 11 and N(F) ≥ 14, using
    - an explicitly constructive algebraic function field [i]

(34−22, 34, 23)-Net in Base 2 — Upper bound on s

There is no (12, 34, 24)-net in base 2, because

extracting embedded OOA [i] would yield OOA(2³⁴, 24, S₂, 2, 22), but
- the linear programming bound for OOAs shows that MÂ â‰¥ 559937 506776 335806 423325 736960 / 30 153402 781214 095699 > 2³⁴ [i]