MinT - Best Known (247−46, 247, s)-Nets in Base 2

Best Known (247−46, 247, s)-Nets in Base 2

(247−46, 247, 320)-Net over F₂ — Constructive and digital

Digital (201, 247, 320)-net over F₂, using

2² times duplication [i] based on digital (199, 245, 320)-net over F₂, using
- trace code for nets [i] based on digital (3, 49, 64)-net over F₃₂, using
  - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(247−46, 247, 776)-Net over F₂ — Digital

Digital (201, 247, 776)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−46, 247, 16082)-Net in Base 2 — Upper bound on s

There is no (201, 247, 16083)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 226 475918 127584 923096 813841 904134 457811 979926 887116 929085 467095 755124 733184 > 2²⁴⁷ [i]