MinT - Best Known (124−30, 124, s)-Nets in Base 2

Best Known (124−30, 124, s)-Nets in Base 2

(124−30, 124, 144)-Net over F₂ — Constructive and digital

Digital (94, 124, 144)-net over F₂, using

2¹ times duplication [i] based on digital (93, 123, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 41, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(124−30, 124, 207)-Net over F₂ — Digital

Digital (94, 124, 207)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−30, 124, 1956)-Net in Base 2 — Upper bound on s

There is no (94, 124, 1957)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 21 370993 611095 112684 006287 933834 832480 > 2¹²⁴ [i]