MinT - Best Known (251−46, 251, s)-Nets in Base 2

Best Known (251−46, 251, s)-Nets in Base 2

(251−46, 251, 320)-Net over F₂ — Constructive and digital

Digital (205, 251, 320)-net over F₂, using

2¹ times duplication [i] based on digital (204, 250, 320)-net over F₂, using
- t-expansion [i] based on digital (203, 250, 320)-net over F₂, using
  - trace code for nets [i] based on digital (3, 50, 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]

(251−46, 251, 830)-Net over F₂ — Digital

Digital (205, 251, 830)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(251−46, 251, 18146)-Net in Base 2 — Upper bound on s

There is no (205, 251, 18147)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3619 914145 426903 797486 640320 987225 928288 469710 287533 686416 878644 514277 675920 > 2²⁵¹ [i]