MinT - Best Known (104, 104+31, s)-Nets in Base 2

Best Known (104, 104+31, s)-Nets in Base 2

(104, 104+31, 195)-Net over F₂ — Constructive and digital

Digital (104, 135, 195)-net over F₂, using

trace code for nets [i] based on digital (14, 45, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(104, 104+31, 255)-Net over F₂ — Digital

Digital (104, 135, 255)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(104, 104+31, 3118)-Net in Base 2 — Upper bound on s

There is no (104, 135, 3119)-net in base 2, because

1 times m-reduction [i] would yield (104, 134, 3119)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 21846 163264 863059 664615 680879 803094 948598 > 2¹³⁴ [i]