MinT - Best Known (136−36, 136, s)-Nets in Base 2

Best Known (136−36, 136, s)-Nets in Base 2

(136−36, 136, 135)-Net over F₂ — Constructive and digital

Digital (100, 136, 135)-net over F₂, using

2¹ times duplication [i] based on digital (99, 135, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 45, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(136−36, 136, 178)-Net over F₂ — Digital

Digital (100, 136, 178)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−36, 136, 1394)-Net in Base 2 — Upper bound on s

There is no (100, 136, 1395)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 87474 094530 960776 898970 576626 642671 207903 > 2¹³⁶ [i]