MinT - Best Known (147, 147+43, s)-Nets in Base 2

Best Known (147, 147+43, s)-Nets in Base 2

(147, 147+43, 195)-Net over F₂ — Constructive and digital

Digital (147, 190, 195)-net over F₂, using

t-expansion [i] based on digital (146, 190, 195)-net over F₂, using
- 8 times m-reduction [i] based on digital (146, 198, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 66, 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]

(147, 147+43, 348)-Net over F₂ — Digital

Digital (147, 190, 348)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(147, 147+43, 4412)-Net in Base 2 — Upper bound on s

There is no (147, 190, 4413)-net in base 2, because

1 times m-reduction [i] would yield (147, 189, 4413)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 784 710633 904088 003286 513229 044618 005182 068586 202881 212286 > 2¹⁸⁹ [i]