MinT - Best Known (119, 119+89, s)-Nets in Base 2

Best Known (119, 119+89, s)-Nets in Base 2

(119, 119+89, 66)-Net over F₂ — Constructive and digital

Digital (119, 208, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 104, 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]

(119, 119+89, 82)-Net over F₂ — Digital

Digital (119, 208, 82)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+89, 388)-Net in Base 2 — Upper bound on s

There is no (119, 208, 389)-net in base 2, because

1 times m-reduction [i] would yield (119, 207, 389)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 216 965538 060730 170997 725243 281337 185064 117620 574476 635933 338672 > 2²⁰⁷ [i]