MinT - Best Known (87, 87+22, s)-Nets in Base 2

Best Known (87, 87+22, s)-Nets in Base 2

(87, 87+22, 196)-Net over F₂ — Constructive and digital

Digital (87, 109, 196)-net over F₂, using

2¹ times duplication [i] based on digital (86, 108, 196)-net over F₂, using
- trace code for nets [i] based on digital (5, 27, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(87, 87+22, 326)-Net over F₂ — Digital

Digital (87, 109, 326)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 87+22, 4704)-Net in Base 2 — Upper bound on s

There is no (87, 109, 4705)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 650 419692 738268 921382 352451 491104 > 2¹⁰⁹ [i]