MinT - Best Known (12, 12+14, s)-Nets in Base 2

Best Known (12, 12+14, s)-Nets in Base 2

(12, 12+14, 14)-Net over F₂ — Constructive and digital

Digital (12, 26, 14)-net over F₂, using

t-expansion [i] based on digital (11, 26, 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]
- Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]

(12, 12+14, 30)-Net in Base 2 — Upper bound on s

There is no (12, 26, 31)-net in base 2, because

extracting embedded OOA [i] would yield OOA(2²⁶, 31, S₂, 2, 14), but
- the linear programming bound for OOAs shows that MÂ â‰¥ 3653 189056 331776 / 53 701569 > 2²⁶ [i]