MinT - Best Known (246−63, 246, s)-Nets in Base 2

Best Known (246−63, 246, s)-Nets in Base 2

(246−63, 246, 195)-Net over F₂ — Constructive and digital

Digital (183, 246, 195)-net over F₂, using

t-expansion [i] based on digital (182, 246, 195)-net over F₂, using
- 6 times m-reduction [i] based on digital (182, 252, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 84, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]

(246−63, 246, 313)-Net over F₂ — Digital

Digital (183, 246, 313)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−63, 246, 2926)-Net in Base 2 — Upper bound on s

There is no (183, 246, 2927)-net in base 2, because

1 times m-reduction [i] would yield (183, 245, 2927)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 56 566106 020870 957288 089607 666363 535279 187001 029657 708886 628034 934694 546244 > 2²⁴⁵ [i]