MinT - Best Known (150−33, 150, s)-Nets in Base 2

Best Known (150−33, 150, s)-Nets in Base 2

(150−33, 150, 195)-Net over F₂ — Constructive and digital

Digital (117, 150, 195)-net over F₂, using

t-expansion [i] based on digital (116, 150, 195)-net over F₂, using
- 3 times m-reduction [i] based on digital (116, 153, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 51, 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]

(150−33, 150, 312)-Net over F₂ — Digital

Digital (117, 150, 312)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−33, 150, 4300)-Net in Base 2 — Upper bound on s

There is no (117, 150, 4301)-net in base 2, because

1 times m-reduction [i] would yield (117, 149, 4301)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 714 927481 873631 138424 333584 866681 417416 596556 > 2¹⁴⁹ [i]