MinT - Best Known (115, 115+45, s)-Nets in Base 2

Best Known (115, 115+45, s)-Nets in Base 2

(115, 115+45, 112)-Net over F₂ — Constructive and digital

Digital (115, 160, 112)-net over F₂, using

4 times m-reduction [i] based on digital (115, 164, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 82, 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]

(115, 115+45, 173)-Net over F₂ — Digital

Digital (115, 160, 173)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 115+45, 1324)-Net in Base 2 — Upper bound on s

There is no (115, 160, 1325)-net in base 2, because

1 times m-reduction [i] would yield (115, 159, 1325)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 736281 166668 405020 489116 305005 325486 213711 693936 > 2¹⁵⁹ [i]