MinT - Best Known (107, 107+37, s)-Nets in Base 2

Best Known (107, 107+37, s)-Nets in Base 2

(107, 107+37, 144)-Net over F₂ — Constructive and digital

Digital (107, 144, 144)-net over F₂, using

trace code for nets [i] based on digital (11, 48, 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]

(107, 107+37, 201)-Net over F₂ — Digital

Digital (107, 144, 201)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 107+37, 1834)-Net in Base 2 — Upper bound on s

There is no (107, 144, 1835)-net in base 2, because

1 times m-reduction [i] would yield (107, 143, 1835)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 11 232560 896357 657505 119812 301670 440859 388130 > 2¹⁴³ [i]