MinT - Best Known (26, 26+21, s)-Nets in Base 2

Best Known (26, 26+21, s)-Nets in Base 2

(26, 26+21, 24)-Net over F₂ — Constructive and digital

Digital (26, 47, 24)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 17, 13)-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]

(26, 26+21, 25)-Net over F₂ — Digital

Digital (26, 47, 25)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(26, 26+21, 96)-Net in Base 2 — Upper bound on s

There is no (26, 47, 97)-net in base 2, because

1 times m-reduction [i] would yield (26, 46, 97)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 76 176081 152736 > 2⁴⁶ [i]