MinT - Best Known (227−97, 227, s)-Nets in Base 2

Best Known (227−97, 227, s)-Nets in Base 2

(227−97, 227, 66)-Net over F₂ — Constructive and digital

Digital (130, 227, 66)-net over F₂, using

3 times m-reduction [i] based on digital (130, 230, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 115, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(227−97, 227, 88)-Net over F₂ — Digital

Digital (130, 227, 88)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(227−97, 227, 422)-Net in Base 2 — Upper bound on s

There is no (130, 227, 423)-net in base 2, because

1 times m-reduction [i] would yield (130, 226, 423)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 109 347155 248566 303878 058793 368763 273424 319172 111916 972445 004162 508824 > 2²²⁶ [i]