MinT - Best Known (158−59, 158, s)-Nets in Base 2

Best Known (158−59, 158, s)-Nets in Base 2

(158−59, 158, 66)-Net over F₂ — Constructive and digital

Digital (99, 158, 66)-net over F₂, using

10 times m-reduction [i] based on digital (99, 168, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 84, 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]

(158−59, 158, 89)-Net over F₂ — Digital

Digital (99, 158, 89)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−59, 158, 456)-Net in Base 2 — Upper bound on s

There is no (99, 158, 457)-net in base 2, because

1 times m-reduction [i] would yield (99, 157, 457)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 191763 035361 127263 524047 331753 769812 744892 449760 > 2¹⁵⁷ [i]