MinT - Best Known (191−43, 191, s)-Nets in Base 2

Best Known (191−43, 191, s)-Nets in Base 2

(191−43, 191, 195)-Net over F₂ — Constructive and digital

Digital (148, 191, 195)-net over F₂, using

10 times m-reduction [i] based on digital (148, 201, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 67, 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]

(191−43, 191, 355)-Net over F₂ — Digital

Digital (148, 191, 355)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(191−43, 191, 4562)-Net in Base 2 — Upper bound on s

There is no (148, 191, 4563)-net in base 2, because

1 times m-reduction [i] would yield (148, 190, 4563)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1575 716984 248318 281855 433222 255188 870141 190870 974887 399056 > 2¹⁹⁰ [i]