MinT - Best Known (191, 191+49, s)-Nets in Base 2

Best Known (191, 191+49, s)-Nets in Base 2

(191, 191+49, 260)-Net over F₂ — Constructive and digital

Digital (191, 240, 260)-net over F₂, using

t-expansion [i] based on digital (189, 240, 260)-net over F₂, using
- 4 times m-reduction [i] based on digital (189, 244, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 61, 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]

(191, 191+49, 567)-Net over F₂ — Digital

Digital (191, 240, 567)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(191, 191+49, 9717)-Net in Base 2 — Upper bound on s

There is no (191, 240, 9718)-net in base 2, because

1 times m-reduction [i] would yield (191, 239, 9718)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 885284 946078 403114 550131 949955 175749 111136 045438 788569 453914 190923 069228 > 2²³⁹ [i]