MinT - Best Known (221−44, 221, s)-Nets in Base 2

Best Known (221−44, 221, s)-Nets in Base 2

(221−44, 221, 260)-Net over F₂ — Constructive and digital

Digital (177, 221, 260)-net over F₂, using

7 times m-reduction [i] based on digital (177, 228, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 57, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(221−44, 221, 572)-Net over F₂ — Digital

Digital (177, 221, 572)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−44, 221, 9535)-Net in Base 2 — Upper bound on s

There is no (177, 221, 9536)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 370917 636511 828893 094870 277295 142776 076155 806862 154373 004599 680341 > 2²²¹ [i]