MinT - Best Known (158−68, 158, s)-Nets in Base 2

Best Known (158−68, 158, s)-Nets in Base 2

(158−68, 158, 54)-Net over F₂ — Constructive and digital

Digital (90, 158, 54)-net over F₂, using

2 times m-reduction [i] based on digital (90, 160, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 80, 27)-net over F₄, using
  - net from sequence [i] based on digital (10, 26)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]

(158−68, 158, 64)-Net over F₂ — Digital

Digital (90, 158, 64)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−68, 158, 291)-Net in Base 2 — Upper bound on s

There is no (90, 158, 292)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 372141 549554 181187 598879 180072 044355 158719 294075 > 2¹⁵⁸ [i]