MinT - Best Known (35−15, 35, s)-Nets in Base 2

Best Known (35−15, 35, s)-Nets in Base 2

(35−15, 35, 23)-Net over F₂ — Constructive and digital

Digital (20, 35, 23)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (4, 11, 11)-net over F₂, using
  - a shift-net [i]
2. digital (9, 24, 12)-net over F₂, using
  - net from sequence [i] based on digital (9, 11)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 9 and N(F) ≥ 12, using
      - an explicitly constructive algebraic function field [i]
  - Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]

(35−15, 35, 88)-Net in Base 2 — Upper bound on s

There is no (20, 35, 89)-net in base 2, because

1 times m-reduction [i] would yield (20, 34, 89)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 17943 131136 > 2³⁴ [i]