MinT - Best Known (207−60, 207, s)-Nets in Base 2

Best Known (207−60, 207, s)-Nets in Base 2

(207−60, 207, 135)-Net over F₂ — Constructive and digital

Digital (147, 207, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 69, 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]

(207−60, 207, 200)-Net over F₂ — Digital

Digital (147, 207, 200)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−60, 207, 1394)-Net in Base 2 — Upper bound on s

There is no (147, 207, 1395)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 207 531453 577821 065100 730708 381928 586687 305367 683534 209737 138920 > 2²⁰⁷ [i]