MinT - Best Known (122−37, 122, s)-Nets in Base 2

Best Known (122−37, 122, s)-Nets in Base 2

(122−37, 122, 72)-Net over F₂ — Constructive and digital

Digital (85, 122, 72)-net over F₂, using

1 times m-reduction [i] based on digital (85, 123, 72)-net over F₂, using
- trace code for nets [i] based on digital (3, 41, 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]

(122−37, 122, 116)-Net over F₂ — Digital

Digital (85, 122, 116)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−37, 122, 771)-Net in Base 2 — Upper bound on s

There is no (85, 122, 772)-net in base 2, because

1 times m-reduction [i] would yield (85, 121, 772)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 696254 642864 995447 573625 455386 509040 > 2¹²¹ [i]