MinT - Best Known (105−67, 105, s)-Nets in Base 2

Best Known (105−67, 105, s)-Nets in Base 2

(105−67, 105, 24)-Net over F₂ — Constructive and digital

Digital (38, 105, 24)-net over F₂, using

t-expansion [i] based on digital (33, 105, 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]

(105−67, 105, 30)-Net over F₂ — Digital

Digital (38, 105, 30)-net over F₂, using

t-expansion [i] based on digital (36, 105, 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]

(105−67, 105, 75)-Net in Base 2 — Upper bound on s

There is no (38, 105, 76)-net in base 2, because

1 times m-reduction [i] would yield (38, 104, 76)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 22 404744 104416 058399 171764 640630 > 2¹⁰⁴ [i]