MinT - Best Known (194−47, 194, s)-Nets in Base 2

Best Known (194−47, 194, s)-Nets in Base 2

(194−47, 194, 195)-Net over F₂ — Constructive and digital

Digital (147, 194, 195)-net over F₂, using

t-expansion [i] based on digital (146, 194, 195)-net over F₂, using
- 4 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]

(194−47, 194, 297)-Net over F₂ — Digital

Digital (147, 194, 297)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−47, 194, 3132)-Net in Base 2 — Upper bound on s

There is no (147, 194, 3133)-net in base 2, because

1 times m-reduction [i] would yield (147, 193, 3133)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12644 115642 131309 001460 450193 877544 079569 553516 443566 364904 > 2¹⁹³ [i]