MinT - Best Known (121, 121+39, s)-Nets in Base 2

Best Known (121, 121+39, s)-Nets in Base 2

(121, 121+39, 195)-Net over F₂ — Constructive and digital

Digital (121, 160, 195)-net over F₂, using

2¹ times duplication [i] based on digital (120, 159, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 53, 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]

(121, 121+39, 249)-Net over F₂ — Digital

Digital (121, 160, 249)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(121, 121+39, 2592)-Net in Base 2 — Upper bound on s

There is no (121, 160, 2593)-net in base 2, because

1 times m-reduction [i] would yield (121, 159, 2593)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 733419 688107 039586 467036 447181 423928 402192 217392 > 2¹⁵⁹ [i]