MinT - Best Known (93, 93+163, s)-Nets in Base 2

Best Known (93, 93+163, s)-Nets in Base 2

(93, 93+163, 53)-Net over F₂ — Constructive and digital

Digital (93, 256, 53)-net over F₂, using

t-expansion [i] based on digital (90, 256, 53)-net over F₂, using
- net from sequence [i] based on digital (90, 52)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 69, N(F)Â =Â 48, 1 place with degree 2, and 4 places with degree 6 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]

(93, 93+163, 60)-Net over F₂ — Digital

Digital (93, 256, 60)-net over F₂, using

t-expansion [i] based on digital (92, 256, 60)-net over F₂, using
- net from sequence [i] based on digital (92, 59)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 92 and N(F) ≥ 60, using
    - Drinfeld modules of rank 1 [i]

(93, 93+163, 173)-Net in Base 2 — Upper bound on s

There is no (93, 256, 174)-net in base 2, because

1 times m-reduction [i] would yield (93, 255, 174)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 70395 655901 892380 231903 045400 129160 137923 466194 532391 325830 057047 884146 431700 > 2²⁵⁵ [i]