MinT - Best Known (15, 15+13, s)-Nets in Base 2

Best Known (15, 15+13, s)-Nets in Base 2

(15, 15+13, 19)-Net over F₂ — Constructive and digital

Digital (15, 28, 19)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (3, 9, 9)-net over F₂, using
  - a shift-net [i]
2. digital (6, 19, 10)-net over F₂, using
  - net from sequence [i] based on digital (6, 9)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, using
      - an explicitly constructive algebraic function field [i]
  - Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]

(15, 15+13, 59)-Net in Base 2 — Upper bound on s

There is no (15, 28, 60)-net in base 2, because

1 times m-reduction [i] would yield (15, 27, 60)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 138 065138 > 2²⁷ [i]