MinT - Best Known (25, 46, s)-Nets in Base 2

Best Known (25, 46, s)-Nets in Base 2

(25, 46, 23)-Net over F₂ — Constructive and digital

Digital (25, 46, 23)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (6, 16, 11)-net over F₂, using
  - linear code embedding found in a computer search [i]
2. digital (9, 30, 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]

(25, 46, 24)-Net over F₂ — Digital

Digital (25, 46, 24)-net over F₂, using

net from sequence [i] based on digital (25, 23)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 25 and N(F) ≥ 24, using
  - Drinfeld modules of rank 1 [i]

(25, 46, 88)-Net in Base 2 — Upper bound on s

There is no (25, 46, 89)-net in base 2, because

1 times m-reduction [i] would yield (25, 45, 89)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 35 774796 601908 > 2⁴⁵ [i]