MinT - Best Known (171, 171+43, s)-Nets in Base 2

Best Known (171, 171+43, s)-Nets in Base 2

(171, 171+43, 260)-Net over F₂ — Constructive and digital

Digital (171, 214, 260)-net over F₂, using

6 times m-reduction [i] based on digital (171, 220, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 55, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(171, 171+43, 542)-Net over F₂ — Digital

Digital (171, 214, 542)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(171, 171+43, 9781)-Net in Base 2 — Upper bound on s

There is no (171, 214, 9782)-net in base 2, because

1 times m-reduction [i] would yield (171, 213, 9782)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13165 956797 623070 615585 543096 473450 992848 867708 550148 771623 867349 > 2²¹³ [i]