MinT - Best Known (186−48, 186, s)-Nets in Base 2

Best Known (186−48, 186, s)-Nets in Base 2

(186−48, 186, 195)-Net over F₂ — Constructive and digital

Digital (138, 186, 195)-net over F₂, using

trace code for nets [i] based on digital (14, 62, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(186−48, 186, 243)-Net over F₂ — Digital

Digital (138, 186, 243)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−48, 186, 2075)-Net in Base 2 — Upper bound on s

There is no (138, 186, 2076)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 99 116707 215350 814397 478807 098809 797473 203111 508725 949421 > 2¹⁸⁶ [i]