MinT - Best Known (51−23, 51, s)-Nets in Base 2

Best Known (51−23, 51, s)-Nets in Base 2

(51−23, 51, 24)-Net over F₂ — Constructive and digital

Digital (28, 51, 24)-net over F₂, using

2¹ times duplication [i] based on digital (27, 50, 24)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (7, 18, 12)-net over F₂, using
    - linear code embedding found in a computer search [i]
  2. digital (9, 32, 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]

(51−23, 51, 26)-Net over F₂ — Digital

Digital (28, 51, 26)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(51−23, 51, 99)-Net in Base 2 — Upper bound on s

There is no (28, 51, 100)-net in base 2, because

1 times m-reduction [i] would yield (28, 50, 100)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1173 056597 910076 > 2⁵⁰ [i]