MinT - Best Known (128, 128+93, s)-Nets in Base 2

Best Known (128, 128+93, s)-Nets in Base 2

(128, 128+93, 66)-Net over F₂ — Constructive and digital

Digital (128, 221, 66)-net over F₂, using

5 times m-reduction [i] based on digital (128, 226, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 113, 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]

(128, 128+93, 89)-Net over F₂ — Digital

Digital (128, 221, 89)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 128+93, 430)-Net in Base 2 — Upper bound on s

There is no (128, 221, 431)-net in base 2, because

1 times m-reduction [i] would yield (128, 220, 431)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 699147 682601 322037 384920 403710 679576 758285 872993 084908 775239 074209 > 2²²⁰ [i]