MinT - Best Known (19, 19+47, s)-Nets in Base 7

Best Known (19, 19+47, s)-Nets in Base 7

(19, 19+47, 27)-Net over F₇ — Constructive and digital

Digital (19, 66, 27)-net over F₇, using

net from sequence [i] based on digital (19, 26)-sequence over F₇, using
- Niederreiter sequence [i]

(19, 19+47, 54)-Net over F₇ — Digital

Digital (19, 66, 54)-net over F₇, using

net from sequence [i] based on digital (19, 53)-sequence over F₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 19 and N(F) ≥ 54, using
  - an algebraic function field by Teo [i]

(19, 19+47, 369)-Net in Base 7 — Upper bound on s

There is no (19, 66, 370)-net in base 7, because

1 times m-reduction [i] would yield (19, 65, 370)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 8 740346 866670 949607 438872 644361 570227 875617 844594 349857 > 7⁶⁵ [i]