MinT - Best Known (27−15, 27, s)-Nets in Base 2

Best Known (27−15, 27, s)-Nets in Base 2

(27−15, 27, 14)-Net over F₂ — Constructive and digital

Digital (12, 27, 14)-net over F₂, using

t-expansion [i] based on digital (11, 27, 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]

(27−15, 27, 29)-Net in Base 2 — Upper bound on s

There is no (12, 27, 30)-net in base 2, because

extracting embedded OOA [i] would yield OOA(2²⁷, 30, S₂, 2, 15), but
- the linear programming bound for OOAs shows that MÂ â‰¥ 636124 921856 / 4013 > 2²⁷ [i]