MinT - Best Known (218−59, 218, s)-Nets in Base 2

Best Known (218−59, 218, s)-Nets in Base 2

(218−59, 218, 144)-Net over F₂ — Constructive and digital

Digital (159, 218, 144)-net over F₂, using

4 times m-reduction [i] based on 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]

(218−59, 218, 246)-Net over F₂ — Digital

Digital (159, 218, 246)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−59, 218, 2045)-Net in Base 2 — Upper bound on s

There is no (159, 218, 2046)-net in base 2, because

1 times m-reduction [i] would yield (159, 217, 2046)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 213432 441812 467287 166632 925791 114901 342904 412988 030660 683779 031773 > 2²¹⁷ [i]