MinT - Best Known (247−42, 247, s)-Nets in Base 2

Best Known (247−42, 247, s)-Nets in Base 2

(247−42, 247, 490)-Net over F₂ — Constructive and digital

Digital (205, 247, 490)-net over F₂, using

2² times duplication [i] based on digital (203, 245, 490)-net over F₂, using
- trace code for nets [i] based on digital (7, 49, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]

(247−42, 247, 1067)-Net over F₂ — Digital

Digital (205, 247, 1067)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−42, 247, 30111)-Net in Base 2 — Upper bound on s

There is no (205, 247, 30112)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 226 239085 013618 005768 059514 545006 217412 232269 700752 808499 561675 381179 447667 > 2²⁴⁷ [i]