MinT - Best Known (122−42, 122, s)-Nets in Base 2

Best Known (122−42, 122, s)-Nets in Base 2

(122−42, 122, 66)-Net over F₂ — Constructive and digital

Digital (80, 122, 66)-net over F₂, using

8 times m-reduction [i] based on digital (80, 130, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 65, 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]

(122−42, 122, 87)-Net over F₂ — Digital

Digital (80, 122, 87)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−42, 122, 456)-Net in Base 2 — Upper bound on s

There is no (80, 122, 457)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 398004 861481 980913 049581 332718 596944 > 2¹²² [i]