MinT - Best Known (169−37, 169, s)-Nets in Base 2

Best Known (169−37, 169, s)-Nets in Base 2

(169−37, 169, 196)-Net over F₂ — Constructive and digital

Digital (132, 169, 196)-net over F₂, using

2¹ times duplication [i] based on digital (131, 168, 196)-net over F₂, using
- trace code for nets [i] based on digital (5, 42, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(169−37, 169, 347)-Net over F₂ — Digital

Digital (132, 169, 347)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−37, 169, 4845)-Net in Base 2 — Upper bound on s

There is no (132, 169, 4846)-net in base 2, because

1 times m-reduction [i] would yield (132, 168, 4846)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 374 185865 742952 254029 475728 845599 936011 332569 341108 > 2¹⁶⁸ [i]