MinT - Best Known (106−29, 106, s)-Nets in Base 2

Best Known (106−29, 106, s)-Nets in Base 2

(106−29, 106, 84)-Net over F₂ — Constructive and digital

Digital (77, 106, 84)-net over F₂, using

2 times m-reduction [i] based on digital (77, 108, 84)-net over F₂, using
- trace code for nets [i] based on digital (5, 36, 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]

(106−29, 106, 135)-Net over F₂ — Digital

Digital (77, 106, 135)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−29, 106, 1074)-Net in Base 2 — Upper bound on s

There is no (77, 106, 1075)-net in base 2, because

1 times m-reduction [i] would yield (77, 105, 1075)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 41 040389 902136 585278 894347 148476 > 2¹⁰⁵ [i]