MinT - Best Known (225−71, 225, s)-Nets in Base 2

Best Known (225−71, 225, s)-Nets in Base 2

(225−71, 225, 112)-Net over F₂ — Constructive and digital

Digital (154, 225, 112)-net over F₂, using

17 times m-reduction [i] based on digital (154, 242, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 121, 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]

(225−71, 225, 175)-Net over F₂ — Digital

Digital (154, 225, 175)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−71, 225, 1123)-Net in Base 2 — Upper bound on s

There is no (154, 225, 1124)-net in base 2, because

1 times m-reduction [i] would yield (154, 224, 1124)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 27 334927 205816 299476 474830 875446 606158 365559 026871 582051 262970 690961 > 2²²⁴ [i]