MinT - Best Known (193−46, 193, s)-Nets in Base 2

Best Known (193−46, 193, s)-Nets in Base 2

(193−46, 193, 195)-Net over F₂ — Constructive and digital

Digital (147, 193, 195)-net over F₂, using

t-expansion [i] based on digital (146, 193, 195)-net over F₂, using
- 5 times m-reduction [i] based on digital (146, 198, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 66, 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]

(193−46, 193, 308)-Net over F₂ — Digital

Digital (147, 193, 308)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−46, 193, 3132)-Net in Base 2 — Upper bound on s

There is no (147, 193, 3133)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12644 115642 131309 001460 450193 877544 079569 553516 443566 364904 > 2¹⁹³ [i]