MinT - Best Known (218−63, 218, s)-Nets in Base 2

Best Known (218−63, 218, s)-Nets in Base 2

(218−63, 218, 135)-Net over F₂ — Constructive and digital

Digital (155, 218, 135)-net over F₂, using

1 times m-reduction [i] based on digital (155, 219, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 73, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(218−63, 218, 210)-Net over F₂ — Digital

Digital (155, 218, 210)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−63, 218, 1544)-Net in Base 2 — Upper bound on s

There is no (155, 218, 1545)-net in base 2, because

1 times m-reduction [i] would yield (155, 217, 1545)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 214624 568578 426834 897511 042759 655938 147451 029944 646349 024009 830400 > 2²¹⁷ [i]