MinT - Best Known (160, 221, s)-Nets in Base 2

Best Known (160, 221, s)-Nets in Base 2

(160, 221, 144)-Net over F₂ — Constructive and digital

Digital (160, 221, 144)-net over F₂, using

t-expansion [i] based on digital (159, 221, 144)-net over F₂, using
- 1 times m-reduction [i] based on digital (159, 222, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 74, 48)-net over F₈, using
    - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
        a function field by SÃ©mirat [i]

(160, 221, 237)-Net over F₂ — Digital

Digital (160, 221, 237)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(160, 221, 1898)-Net in Base 2 — Upper bound on s

There is no (160, 221, 1899)-net in base 2, because

1 times m-reduction [i] would yield (160, 220, 1899)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 701325 108465 361766 665775 849547 696710 126186 254462 726114 381564 924712 > 2²²⁰ [i]