MinT - Best Known (149, 149+61, s)-Nets in Base 2

Best Known (149, 149+61, s)-Nets in Base 2

(149, 149+61, 135)-Net over F₂ — Constructive and digital

Digital (149, 210, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 70, 45)-net over F₈, using
- net from sequence [i] based on digital (9, 44)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
    - an explicitly constructive algebraic function field [i]

(149, 149+61, 201)-Net over F₂ — Digital

Digital (149, 210, 201)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(149, 149+61, 1462)-Net in Base 2 — Upper bound on s

There is no (149, 210, 1463)-net in base 2, because

1 times m-reduction [i] would yield (149, 209, 1463)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 829 743735 612418 787674 560620 202944 353427 631879 686267 619986 339220 > 2²⁰⁹ [i]