MinT - Best Known (149, 149+49, s)-Nets in Base 2

Best Known (149, 149+49, s)-Nets in Base 2

(149, 149+49, 195)-Net over F₂ — Constructive and digital

Digital (149, 198, 195)-net over F₂, using

t-expansion [i] based on digital (148, 198, 195)-net over F₂, using
- 3 times m-reduction [i] based on digital (148, 201, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 67, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]

(149, 149+49, 285)-Net over F₂ — Digital

Digital (149, 198, 285)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(149, 149+49, 2864)-Net in Base 2 — Upper bound on s

There is no (149, 198, 2865)-net in base 2, because

1 times m-reduction [i] would yield (149, 197, 2865)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 202271 493610 565635 083688 825901 227180 413036 526844 818647 074044 > 2¹⁹⁷ [i]