MinT - Best Known (109−71, 109, s)-Nets in Base 2

Best Known (109−71, 109, s)-Nets in Base 2

(109−71, 109, 24)-Net over F₂ — Constructive and digital

Digital (38, 109, 24)-net over F₂, using

t-expansion [i] based on digital (33, 109, 24)-net over F₂, using
- net from sequence [i] based on digital (33, 23)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 33 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]

(109−71, 109, 30)-Net over F₂ — Digital

Digital (38, 109, 30)-net over F₂, using

t-expansion [i] based on digital (36, 109, 30)-net over F₂, using
- net from sequence [i] based on digital (36, 29)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 36 and N(F) ≥ 30, using
    - Drinfeld modules of rank 1 [i]

(109−71, 109, 74)-Net in Base 2 — Upper bound on s

There is no (38, 109, 75)-net in base 2, because

1 times m-reduction [i] would yield (38, 108, 75)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 368 534623 138507 086401 970156 556564 > 2¹⁰⁸ [i]