MinT - Best Known (242−69, 242, s)-Nets in Base 2

Best Known (242−69, 242, s)-Nets in Base 2

(242−69, 242, 144)-Net over F₂ — Constructive and digital

Digital (173, 242, 144)-net over F₂, using

1 times m-reduction [i] based on digital (173, 243, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 81, 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]

(242−69, 242, 237)-Net over F₂ — Digital

Digital (173, 242, 237)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−69, 242, 1791)-Net in Base 2 — Upper bound on s

There is no (173, 242, 1792)-net in base 2, because

1 times m-reduction [i] would yield (173, 241, 1792)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 537371 421533 918338 757991 820125 785619 635724 963307 055025 120630 946041 835225 > 2²⁴¹ [i]