MinT - Best Known (13, 13+39, s)-Nets in Base 7

Best Known (13, 13+39, s)-Nets in Base 7

(13, 13+39, 21)-Net over F₇ — Constructive and digital

Digital (13, 52, 21)-net over F₇, using

net from sequence [i] based on digital (13, 20)-sequence over F₇, using
- Niederreiter sequence [i]

(13, 13+39, 48)-Net over F₇ — Digital

Digital (13, 52, 48)-net over F₇, using

net from sequence [i] based on digital (13, 47)-sequence over F₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 13 and N(F) ≥ 48, using
  - an algebraic function field by Teo [i]

(13, 13+39, 233)-Net in Base 7 — Upper bound on s

There is no (13, 52, 234)-net in base 7, because

1 times m-reduction [i] would yield (13, 51, 234)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 13 387222 537375 295884 954796 376109 966932 517225 > 7⁵¹ [i]