MinT - Best Known (182−53, 182, s)-Nets in Base 2

Best Known (182−53, 182, s)-Nets in Base 2

(182−53, 182, 112)-Net over F₂ — Constructive and digital

Digital (129, 182, 112)-net over F₂, using

10 times m-reduction [i] based on digital (129, 192, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 96, 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]

(182−53, 182, 177)-Net over F₂ — Digital

Digital (129, 182, 177)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−53, 182, 1277)-Net in Base 2 — Upper bound on s

There is no (129, 182, 1278)-net in base 2, because

1 times m-reduction [i] would yield (129, 181, 1278)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 125920 769721 766005 436594 724340 142092 973868 195049 991282 > 2¹⁸¹ [i]