MinT - Best Known (247−56, 247, s)-Nets in Base 2

Best Known (247−56, 247, s)-Nets in Base 2

(247−56, 247, 207)-Net over F₂ — Constructive and digital

Digital (191, 247, 207)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (9, 37, 12)-net over F₂, using
  - net from sequence [i] based on digital (9, 11)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 9 and N(F) ≥ 12, using
      - an explicitly constructive algebraic function field [i]
2. digital (154, 210, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 70, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]

(247−56, 247, 433)-Net over F₂ — Digital

Digital (191, 247, 433)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−56, 247, 5069)-Net in Base 2 — Upper bound on s

There is no (191, 247, 5070)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 226 385245 135309 265510 116332 296868 955618 131035 283347 021277 748873 507131 328284 > 2²⁴⁷ [i]