MinT - Best Known (124−46, 124, s)-Nets in Base 2

Best Known (124−46, 124, s)-Nets in Base 2

(124−46, 124, 66)-Net over F₂ — Constructive and digital

Digital (78, 124, 66)-net over F₂, using

2 times m-reduction [i] based on digital (78, 126, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 63, 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]

(124−46, 124, 74)-Net over F₂ — Digital

Digital (78, 124, 74)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−46, 124, 363)-Net in Base 2 — Upper bound on s

There is no (78, 124, 364)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 22 538663 478395 432907 062221 527427 348572 > 2¹²⁴ [i]