MinT - Best Known (194, 245, s)-Nets in Base 2

Best Known (194, 245, s)-Nets in Base 2

(194, 245, 260)-Net over F₂ — Constructive and digital

Digital (194, 245, 260)-net over F₂, using

t-expansion [i] based on digital (192, 245, 260)-net over F₂, using
- 3 times m-reduction [i] based on digital (192, 248, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 62, 65)-net over F₁₆, using
    - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]

(194, 245, 545)-Net over F₂ — Digital

Digital (194, 245, 545)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(194, 245, 8787)-Net in Base 2 — Upper bound on s

There is no (194, 245, 8788)-net in base 2, because

1 times m-reduction [i] would yield (194, 244, 8788)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 28 322730 365620 124238 247019 542319 322525 179643 170069 852402 700275 942988 752168 > 2²⁴⁴ [i]