MinT - Best Known (206−70, 206, s)-Nets in Base 2

Best Known (206−70, 206, s)-Nets in Base 2

(206−70, 206, 112)-Net over F₂ — Constructive and digital

Digital (136, 206, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 103, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(206−70, 206, 137)-Net over F₂ — Digital

Digital (136, 206, 137)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−70, 206, 771)-Net in Base 2 — Upper bound on s

There is no (136, 206, 772)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 103 841558 520274 703939 331112 698943 042333 545677 574598 168195 150872 > 2²⁰⁶ [i]