MinT - Best Known (211−82, 211, s)-Nets in Base 2

Best Known (211−82, 211, s)-Nets in Base 2

(211−82, 211, 68)-Net over F₂ — Constructive and digital

Digital (129, 211, 68)-net over F₂, using

5 times m-reduction [i] based on digital (129, 216, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 108, 34)-net over F₄, using
  - net from sequence [i] based on digital (21, 33)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
      - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(211−82, 211, 103)-Net over F₂ — Digital

Digital (129, 211, 103)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−82, 211, 513)-Net in Base 2 — Upper bound on s

There is no (129, 211, 514)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3424 970598 784691 220293 156614 515662 695523 146097 804526 096724 161600 > 2²¹¹ [i]