MinT - Best Known (221−69, 221, s)-Nets in Base 2

Best Known (221−69, 221, s)-Nets in Base 2

(221−69, 221, 112)-Net over F₂ — Constructive and digital

Digital (152, 221, 112)-net over F₂, using

17 times m-reduction [i] based on digital (152, 238, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 119, 56)-net over F₄, using
  - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(221−69, 221, 177)-Net over F₂ — Digital

Digital (152, 221, 177)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−69, 221, 1150)-Net in Base 2 — Upper bound on s

There is no (152, 221, 1151)-net in base 2, because

1 times m-reduction [i] would yield (152, 220, 1151)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 693380 649942 462522 413330 544800 003448 125932 633265 810342 907491 173931 > 2²²⁰ [i]