MinT - Best Known (175, 175+78, s)-Nets in Base 2

Best Known (175, 175+78, s)-Nets in Base 2

(175, 175+78, 112)-Net over F₂ — Constructive and digital

Digital (175, 253, 112)-net over F₂, using

t-expansion [i] based on digital (163, 253, 112)-net over F₂, using
- 7 times m-reduction [i] based on digital (163, 260, 112)-net over F₂, using
  - trace code for nets [i] based on digital (33, 130, 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]

(175, 175+78, 204)-Net over F₂ — Digital

Digital (175, 253, 204)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(175, 175+78, 1324)-Net in Base 2 — Upper bound on s

There is no (175, 253, 1325)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14761 031208 743240 481110 124217 982245 405930 188495 008532 250082 736975 382015 305864 > 2²⁵³ [i]