MinT - Best Known (136−31, 136, s)-Nets in Base 2

Best Known (136−31, 136, s)-Nets in Base 2

(136−31, 136, 195)-Net over F₂ — Constructive and digital

Digital (105, 136, 195)-net over F₂, using

2¹ times duplication [i] based on digital (104, 135, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 45, 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]

(136−31, 136, 261)-Net over F₂ — Digital

Digital (105, 136, 261)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−31, 136, 3266)-Net in Base 2 — Upper bound on s

There is no (105, 136, 3267)-net in base 2, because

1 times m-reduction [i] would yield (105, 135, 3267)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 43583 981265 247638 814861 424267 075413 227808 > 2¹³⁵ [i]