MinT - Best Known (186−34, 186, s)-Nets in Base 2

Best Known (186−34, 186, s)-Nets in Base 2

(186−34, 186, 320)-Net over F₂ — Constructive and digital

Digital (152, 186, 320)-net over F₂, using

2¹ times duplication [i] based on digital (151, 185, 320)-net over F₂, using
- trace code for nets [i] based on digital (3, 37, 64)-net over F₃₂, using
  - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(186−34, 186, 662)-Net over F₂ — Digital

Digital (152, 186, 662)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−34, 186, 14086)-Net in Base 2 — Upper bound on s

There is no (152, 186, 14087)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 98 158207 550982 566276 071952 351117 242715 522729 749318 139264 > 2¹⁸⁶ [i]