MinT - Best Known (157−41, 157, s)-Nets in Base 2

Best Known (157−41, 157, s)-Nets in Base 2

(157−41, 157, 144)-Net over F₂ — Constructive and digital

Digital (116, 157, 144)-net over F₂, using

2¹ times duplication [i] based on digital (115, 156, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 52, 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]

(157−41, 157, 206)-Net over F₂ — Digital

Digital (116, 157, 206)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−41, 157, 1821)-Net in Base 2 — Upper bound on s

There is no (116, 157, 1822)-net in base 2, because

1 times m-reduction [i] would yield (116, 156, 1822)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 91908 103134 540884 536198 304307 576905 211990 670781 > 2¹⁵⁶ [i]