MinT - Best Known (206−88, 206, s)-Nets in Base 2

Best Known (206−88, 206, s)-Nets in Base 2

(206−88, 206, 66)-Net over F₂ — Constructive and digital

Digital (118, 206, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 103, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(206−88, 206, 81)-Net over F₂ — Digital

Digital (118, 206, 81)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−88, 206, 381)-Net in Base 2 — Upper bound on s

There is no (118, 206, 382)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 108 281135 681125 838540 035802 167193 363909 644684 259728 234437 582175 > 2²⁰⁶ [i]