MinT - Best Known (87, 87+30, s)-Nets in Base 2

Best Known (87, 87+30, s)-Nets in Base 2

(87, 87+30, 135)-Net over F₂ — Constructive and digital

Digital (87, 117, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 39, 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]

(87, 87+30, 171)-Net over F₂ — Digital

Digital (87, 117, 171)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 87+30, 1409)-Net in Base 2 — Upper bound on s

There is no (87, 117, 1410)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 166707 347896 114736 964242 417472 543040 > 2¹¹⁷ [i]