MinT - Best Known (249−74, 249, s)-Nets in Base 2

Best Known (249−74, 249, s)-Nets in Base 2

(249−74, 249, 135)-Net over F₂ — Constructive and digital

Digital (175, 249, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 83, 45)-net over F₈, using
- net from sequence [i] based on digital (9, 44)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
    - an explicitly constructive algebraic function field [i]

(249−74, 249, 220)-Net over F₂ — Digital

Digital (175, 249, 220)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−74, 249, 1500)-Net in Base 2 — Upper bound on s

There is no (175, 249, 1501)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 904 865048 840648 774467 938444 032156 066044 214002 913668 699683 072784 059019 116132 > 2²⁴⁹ [i]