MinT - Best Known (223−62, 223, s)-Nets in Base 2

Best Known (223−62, 223, s)-Nets in Base 2

(223−62, 223, 144)-Net over F₂ — Constructive and digital

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]

(223−62, 223, 235)-Net over F₂ — Digital

Digital (161, 223, 235)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−62, 223, 1772)-Net in Base 2 — Upper bound on s

There is no (161, 223, 1773)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13 674208 541617 982498 583608 056197 947235 626623 924283 286010 851046 633168 > 2²²³ [i]