MinT - Best Known (103−29, 103, s)-Nets in Base 2

Best Known (103−29, 103, s)-Nets in Base 2

(103−29, 103, 84)-Net over F₂ — Constructive and digital

Digital (74, 103, 84)-net over F₂, using

2¹ times duplication [i] based on digital (73, 102, 84)-net over F₂, using
- trace code for nets [i] based on digital (5, 34, 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]

(103−29, 103, 124)-Net over F₂ — Digital

Digital (74, 103, 124)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(103−29, 103, 923)-Net in Base 2 — Upper bound on s

There is no (74, 103, 924)-net in base 2, because

1 times m-reduction [i] would yield (74, 102, 924)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 142074 222721 000012 664635 667212 > 2¹⁰² [i]