MinT - Best Known (182−77, 182, s)-Nets in Base 2

Best Known (182−77, 182, s)-Nets in Base 2

(182−77, 182, 60)-Net over F₂ — Constructive and digital

Digital (105, 182, 60)-net over F₂, using

2 times m-reduction [i] based on digital (105, 184, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 92, 30)-net over F₄, using
  - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
      - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(182−77, 182, 75)-Net over F₂ — Digital

Digital (105, 182, 75)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−77, 182, 354)-Net in Base 2 — Upper bound on s

There is no (105, 182, 355)-net in base 2, because

1 times m-reduction [i] would yield (105, 181, 355)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 116357 150487 611145 554360 495940 940512 538169 749463 035584 > 2¹⁸¹ [i]