MinT - Best Known (105−29, 105, s)-Nets in Base 2

Best Known (105−29, 105, s)-Nets in Base 2

(105−29, 105, 84)-Net over F₂ — Constructive and digital

Digital (76, 105, 84)-net over F₂, using

t-expansion [i] based on digital (75, 105, 84)-net over F₂, using
- trace code for nets [i] based on digital (5, 35, 28)-net over F₈, using
  - net from sequence [i] based on digital (5, 27)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
      - a function field by SÃ©mirat [i]

(105−29, 105, 132)-Net over F₂ — Digital

Digital (76, 105, 132)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−29, 105, 1021)-Net in Base 2 — Upper bound on s

There is no (76, 105, 1022)-net in base 2, because

1 times m-reduction [i] would yield (76, 104, 1022)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 20 492933 375832 771441 430510 498368 > 2¹⁰⁴ [i]