MinT - Best Known (87−24, 87, s)-Nets in Base 2

Best Known (87−24, 87, s)-Nets in Base 2

(87−24, 87, 84)-Net over F₂ — Constructive and digital

Digital (63, 87, 84)-net over F₂, using

trace code for nets [i] based on digital (5, 29, 28)-net over F₈, using
- net from sequence [i] based on digital (5, 27)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
    - a function field by SÃ©mirat [i]

(87−24, 87, 114)-Net over F₂ — Digital

Digital (63, 87, 114)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−24, 87, 787)-Net in Base 2 — Upper bound on s

There is no (63, 87, 788)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 155 365302 220692 922071 804564 > 2⁸⁷ [i]