MinT - Best Known (125−28, 125, s)-Nets in Base 2

Best Known (125−28, 125, s)-Nets in Base 2

(125−28, 125, 152)-Net over F₂ — Constructive and digital

Digital (97, 125, 152)-net over F₂, using

2¹ times duplication [i] based on digital (96, 124, 152)-net over F₂, using
- trace code for nets [i] based on digital (3, 31, 38)-net over F₁₆, using
  - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(125−28, 125, 258)-Net over F₂ — Digital

Digital (97, 125, 258)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−28, 125, 2925)-Net in Base 2 — Upper bound on s

There is no (97, 125, 2926)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 42 633329 056211 000499 669629 370997 383144 > 2¹²⁵ [i]