MinT - Best Known (222−63, 222, s)-Nets in Base 2

Best Known (222−63, 222, s)-Nets in Base 2

(222−63, 222, 144)-Net over F₂ — Constructive and digital

Digital (159, 222, 144)-net over F₂, using

trace code for nets [i] based on digital (11, 74, 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]

(222−63, 222, 223)-Net over F₂ — Digital

Digital (159, 222, 223)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−63, 222, 1692)-Net in Base 2 — Upper bound on s

There is no (159, 222, 1693)-net in base 2, because

1 times m-reduction [i] would yield (159, 221, 1693)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 388536 554740 139795 367046 355095 764818 320280 890723 646775 090060 164920 > 2²²¹ [i]