MinT - Best Known (84, 84+55, s)-Nets in Base 2

Best Known (84, 84+55, s)-Nets in Base 2

(84, 84+55, 60)-Net over F₂ — Constructive and digital

Digital (84, 139, 60)-net over F₂, using

3 times m-reduction [i] based on digital (84, 142, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 71, 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]

(84, 84+55, 70)-Net over F₂ — Digital

Digital (84, 139, 70)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+55, 339)-Net in Base 2 — Upper bound on s

There is no (84, 139, 340)-net in base 2, because

1 times m-reduction [i] would yield (84, 138, 340)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 363675 266221 930133 789723 712644 873126 410520 > 2¹³⁸ [i]