MinT - Best Known (111, 142, s)-Nets in Base 2

Best Known (111, 142, s)-Nets in Base 2

(111, 142, 195)-Net over F₂ — Constructive and digital

Digital (111, 142, 195)-net over F₂, using

t-expansion [i] based on digital (110, 142, 195)-net over F₂, using
- 2 times m-reduction [i] based on digital (110, 144, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 48, 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]

(111, 142, 306)-Net over F₂ — Digital

Digital (111, 142, 306)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 142, 4317)-Net in Base 2 — Upper bound on s

There is no (111, 142, 4318)-net in base 2, because

1 times m-reduction [i] would yield (111, 141, 4318)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 791069 744001 499270 841142 670272 250097 271308 > 2¹⁴¹ [i]