MinT - Best Known (135−44, 135, s)-Nets in Base 2

Best Known (135−44, 135, s)-Nets in Base 2

(135−44, 135, 68)-Net over F₂ — Constructive and digital

Digital (91, 135, 68)-net over F₂, using

5 times m-reduction [i] based on digital (91, 140, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 70, 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]

(135−44, 135, 107)-Net over F₂ — Digital

Digital (91, 135, 107)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−44, 135, 605)-Net in Base 2 — Upper bound on s

There is no (91, 135, 606)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 44851 674979 718746 585523 193649 239265 596052 > 2¹³⁵ [i]