MinT - Best Known (170−47, 170, s)-Nets in Base 2

Best Known (170−47, 170, s)-Nets in Base 2

(170−47, 170, 135)-Net over F₂ — Constructive and digital

Digital (123, 170, 135)-net over F₂, using

1 times m-reduction [i] based on digital (123, 171, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 57, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(170−47, 170, 189)-Net over F₂ — Digital

Digital (123, 170, 189)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−47, 170, 1502)-Net in Base 2 — Upper bound on s

There is no (123, 170, 1503)-net in base 2, because

1 times m-reduction [i] would yield (123, 169, 1503)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 756 484223 434461 694471 969429 264690 624170 500286 622598 > 2¹⁶⁹ [i]