MinT - Best Known (162, 162+61, s)-Nets in Base 2

Best Known (162, 162+61, s)-Nets in Base 2

(162, 162+61, 144)-Net over F₂ — Constructive and digital

Digital (162, 223, 144)-net over F₂, using

t-expansion [i] based on digital (161, 223, 144)-net over F₂, using
- 2 times m-reduction [i] based on digital (161, 225, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 75, 48)-net over F₈, using
    - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
        a function field by SÃ©mirat [i]

(162, 162+61, 244)-Net over F₂ — Digital

Digital (162, 223, 244)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 162+61, 1990)-Net in Base 2 — Upper bound on s

There is no (162, 223, 1991)-net in base 2, because

1 times m-reduction [i] would yield (162, 222, 1991)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 817975 936243 351436 037530 178336 797032 279608 957311 203647 968153 802600 > 2²²² [i]