MinT - Best Known (87, 87+45, s)-Nets in Base 2

Best Known (87, 87+45, s)-Nets in Base 2

(87, 87+45, 68)-Net over F₂ — Constructive and digital

Digital (87, 132, 68)-net over F₂, using

trace code for nets [i] based on digital (21, 66, 34)-net over F₄, using
- net from sequence [i] based on digital (21, 33)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
    - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(87, 87+45, 94)-Net over F₂ — Digital

Digital (87, 132, 94)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 87+45, 529)-Net in Base 2 — Upper bound on s

There is no (87, 132, 530)-net in base 2, because

1 times m-reduction [i] would yield (87, 131, 530)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2740 371253 139960 892012 160828 816665 148416 > 2¹³¹ [i]