MinT - Best Known (223−65, 223, s)-Nets in Base 2

Best Known (223−65, 223, s)-Nets in Base 2

(223−65, 223, 135)-Net over F₂ — Constructive and digital

Digital (158, 223, 135)-net over F₂, using

2¹ times duplication [i] based on digital (157, 222, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 74, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(223−65, 223, 210)-Net over F₂ — Digital

Digital (158, 223, 210)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−65, 223, 1520)-Net in Base 2 — Upper bound on s

There is no (158, 223, 1521)-net in base 2, because

1 times m-reduction [i] would yield (158, 222, 1521)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 754434 040845 972959 841949 354869 814890 478876 454294 418885 746432 696533 > 2²²² [i]