MinT - Best Known (163−41, 163, s)-Nets in Base 2

Best Known (163−41, 163, s)-Nets in Base 2

(163−41, 163, 144)-Net over F₂ — Constructive and digital

Digital (122, 163, 144)-net over F₂, using

t-expansion [i] based on digital (121, 163, 144)-net over F₂, using
- 2 times m-reduction [i] based on digital (121, 165, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 55, 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]

(163−41, 163, 234)-Net over F₂ — Digital

Digital (122, 163, 234)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−41, 163, 2249)-Net in Base 2 — Upper bound on s

There is no (122, 163, 2250)-net in base 2, because

1 times m-reduction [i] would yield (122, 162, 2250)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 888561 167396 974394 156828 616011 028605 449681 209176 > 2¹⁶² [i]