MinT - Best Known (226−64, 226, s)-Nets in Base 2

Best Known (226−64, 226, s)-Nets in Base 2

(226−64, 226, 144)-Net over F₂ — Constructive and digital

Digital (162, 226, 144)-net over F₂, using

2¹ times duplication [i] based on digital (161, 225, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 75, 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]

(226−64, 226, 227)-Net over F₂ — Digital

Digital (162, 226, 227)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−64, 226, 1662)-Net in Base 2 — Upper bound on s

There is no (162, 226, 1663)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 108 375284 749235 903187 776326 772248 218972 722935 552797 717272 864287 096101 > 2²²⁶ [i]