MinT - Best Known (115, 115+41, s)-Nets in Base 2

Best Known (115, 115+41, s)-Nets in Base 2

(115, 115+41, 144)-Net over F₂ — Constructive and digital

Digital (115, 156, 144)-net over F₂, using

trace code for nets [i] based on digital (11, 52, 48)-net over F₈, using
- net from sequence [i] based on digital (11, 47)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
    - a function field by SÃ©mirat [i]

(115, 115+41, 201)-Net over F₂ — Digital

Digital (115, 156, 201)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 115+41, 1758)-Net in Base 2 — Upper bound on s

There is no (115, 156, 1759)-net in base 2, because

1 times m-reduction [i] would yield (115, 155, 1759)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 45981 940695 647139 774193 108868 406592 387582 224283 > 2¹⁵⁵ [i]