MinT - Best Known (101−67, 101, s)-Nets in Base 2

Best Known (101−67, 101, s)-Nets in Base 2

(101−67, 101, 24)-Net over F₂ — Constructive and digital

Digital (34, 101, 24)-net over F₂, using

t-expansion [i] based on digital (33, 101, 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]

(101−67, 101, 28)-Net over F₂ — Digital

Digital (34, 101, 28)-net over F₂, using

t-expansion [i] based on digital (33, 101, 28)-net over F₂, using
- net from sequence [i] based on digital (33, 27)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 33 and N(F) ≥ 28, using
    - Drinfeld modules of rank 1 [i]

(101−67, 101, 66)-Net in Base 2 — Upper bound on s

There is no (34, 101, 67)-net in base 2, because

1 times m-reduction [i] would yield (34, 100, 67)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 354088 077642 809005 218098 913880 > 2¹⁰⁰ [i]