MinT - Best Known (128, 128+55, s)-Nets in Base 2

Best Known (128, 128+55, s)-Nets in Base 2

(128, 128+55, 112)-Net over F₂ — Constructive and digital

Digital (128, 183, 112)-net over F₂, using

7 times m-reduction [i] based on digital (128, 190, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 95, 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]

(128, 128+55, 165)-Net over F₂ — Digital

Digital (128, 183, 165)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 128+55, 1128)-Net in Base 2 — Upper bound on s

There is no (128, 183, 1129)-net in base 2, because

1 times m-reduction [i] would yield (128, 182, 1129)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 135428 727411 875403 692803 912060 230140 754461 378732 395888 > 2¹⁸² [i]