MinT - Best Known (135, 135+39, s)-Nets in Base 2

Best Known (135, 135+39, s)-Nets in Base 2

(135, 135+39, 195)-Net over F₂ — Constructive and digital

Digital (135, 174, 195)-net over F₂, using

t-expansion [i] based on digital (134, 174, 195)-net over F₂, using
- 6 times m-reduction [i] based on digital (134, 180, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 60, 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]

(135, 135+39, 333)-Net over F₂ — Digital

Digital (135, 174, 333)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+39, 4338)-Net in Base 2 — Upper bound on s

There is no (135, 174, 4339)-net in base 2, because

1 times m-reduction [i] would yield (135, 173, 4339)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 11973 803454 109370 719808 924284 044408 862191 876416 382386 > 2¹⁷³ [i]