MinT - Best Known (132−41, 132, s)-Nets in Base 2

Best Known (132−41, 132, s)-Nets in Base 2

(132−41, 132, 72)-Net over F₂ — Constructive and digital

Digital (91, 132, 72)-net over F₂, using

trace code for nets [i] based on digital (3, 44, 24)-net over F₈, using
- net from sequence [i] based on digital (3, 23)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
    - the Klein quartic over F₈ [i]

(132−41, 132, 117)-Net over F₂ — Digital

Digital (91, 132, 117)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−41, 132, 749)-Net in Base 2 — Upper bound on s

There is no (91, 132, 750)-net in base 2, because

1 times m-reduction [i] would yield (91, 131, 750)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2783 837064 053980 457936 011136 080735 902226 > 2¹³¹ [i]