MinT - Best Known (221−67, 221, s)-Nets in Base 2

Best Known (221−67, 221, s)-Nets in Base 2

(221−67, 221, 112)-Net over F₂ — Constructive and digital

Digital (154, 221, 112)-net over F₂, using

21 times m-reduction [i] based on digital (154, 242, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 121, 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]

(221−67, 221, 189)-Net over F₂ — Digital

Digital (154, 221, 189)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−67, 221, 1289)-Net in Base 2 — Upper bound on s

There is no (154, 221, 1290)-net in base 2, because

1 times m-reduction [i] would yield (154, 220, 1290)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 723656 192836 966633 069940 255371 751812 371304 243956 070072 147399 882152 > 2²²⁰ [i]