MinT - Best Known (217−70, 217, s)-Nets in Base 2

Best Known (217−70, 217, s)-Nets in Base 2

(217−70, 217, 112)-Net over F₂ — Constructive and digital

Digital (147, 217, 112)-net over F₂, using

11 times m-reduction [i] based on digital (147, 228, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 114, 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]

(217−70, 217, 161)-Net over F₂ — Digital

Digital (147, 217, 161)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−70, 217, 971)-Net in Base 2 — Upper bound on s

There is no (147, 217, 972)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 213194 187110 072079 562882 291002 970014 961144 300232 700150 993922 645270 > 2²¹⁷ [i]