MinT - Best Known (91, 91+29, s)-Nets in Base 2

Best Known (91, 91+29, s)-Nets in Base 2

(91, 91+29, 144)-Net over F₂ — Constructive and digital

Digital (91, 120, 144)-net over F₂, using

trace code for nets [i] based on digital (11, 40, 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]

(91, 91+29, 203)-Net over F₂ — Digital

Digital (91, 120, 203)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+29, 2168)-Net in Base 2 — Upper bound on s

There is no (91, 120, 2169)-net in base 2, because

1 times m-reduction [i] would yield (91, 119, 2169)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 667084 800964 816364 810694 399699 091688 > 2¹¹⁹ [i]