MinT - Best Known (96−63, 96, s)-Nets in Base 7

Best Known (96−63, 96, s)-Nets in Base 7

(96−63, 96, 35)-Net over F₇ — Constructive and digital

Digital (33, 96, 35)-net over F₇, using

net from sequence [i] based on digital (33, 34)-sequence over F₇, using
- Niederreiter sequence [i]

(96−63, 96, 96)-Net over F₇ — Digital

Digital (33, 96, 96)-net over F₇, using

net from sequence [i] based on digital (33, 95)-sequence over F₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 33 and N(F) ≥ 96, using
  - an algebraic function field by Teo [i]

(96−63, 96, 784)-Net in Base 7 — Upper bound on s

There is no (33, 96, 785)-net in base 7, because

1 times m-reduction [i] would yield (33, 95, 785)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 193 841443 618137 448353 788709 730528 692777 782001 178935 196628 345046 204148 709918 874679 > 7⁹⁵ [i]