MinT - Best Known (216−57, 216, s)-Nets in Base 2

Best Known (216−57, 216, s)-Nets in Base 2

(216−57, 216, 195)-Net over F₂ — Constructive and digital

Digital (159, 216, 195)-net over F₂, using

t-expansion [i] based on digital (158, 216, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 72, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(216−57, 216, 259)-Net over F₂ — Digital

Digital (159, 216, 259)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−57, 216, 2273)-Net in Base 2 — Upper bound on s

There is no (159, 216, 2274)-net in base 2, because

1 times m-reduction [i] would yield (159, 215, 2274)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 52983 794238 246978 736014 109970 163621 669383 948960 210841 789028 031816 > 2²¹⁵ [i]