MinT - Best Known (231−43, 231, s)-Nets in Base 2

Best Known (231−43, 231, s)-Nets in Base 2

(231−43, 231, 320)-Net over F₂ — Constructive and digital

Digital (188, 231, 320)-net over F₂, using

2¹ times duplication [i] based on digital (187, 230, 320)-net over F₂, using
- trace code for nets [i] based on digital (3, 46, 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]

(231−43, 231, 736)-Net over F₂ — Digital

Digital (188, 231, 736)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−43, 231, 17167)-Net in Base 2 — Upper bound on s

There is no (188, 231, 17168)-net in base 2, because

1 times m-reduction [i] would yield (188, 230, 17168)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1726 671475 162273 808516 646976 731821 380124 407400 732957 419557 483766 587888 > 2²³⁰ [i]