MinT - Best Known (136−34, 136, s)-Nets in Base 2

Best Known (136−34, 136, s)-Nets in Base 2

(136−34, 136, 144)-Net over F₂ — Constructive and digital

Digital (102, 136, 144)-net over F₂, using

2¹ times duplication [i] based on digital (101, 135, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 45, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(136−34, 136, 205)-Net over F₂ — Digital

Digital (102, 136, 205)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−34, 136, 1812)-Net in Base 2 — Upper bound on s

There is no (102, 136, 1813)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 87536 493875 454514 455527 459770 028163 176014 > 2¹³⁶ [i]