MinT - Best Known (153, 153+45, s)-Nets in Base 2

Best Known (153, 153+45, s)-Nets in Base 2

(153, 153+45, 195)-Net over F₂ — Constructive and digital

Digital (153, 198, 195)-net over F₂, using

t-expansion [i] based on digital (152, 198, 195)-net over F₂, using
- 9 times m-reduction [i] based on digital (152, 207, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 69, 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]

(153, 153+45, 356)-Net over F₂ — Digital

Digital (153, 198, 356)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(153, 153+45, 4459)-Net in Base 2 — Upper bound on s

There is no (153, 198, 4460)-net in base 2, because

1 times m-reduction [i] would yield (153, 197, 4460)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 201253 765171 687366 412481 378538 960793 013815 752383 128115 395148 > 2¹⁹⁷ [i]