MinT - Best Known (15, 15+29, s)-Nets in Base 7

Best Known (15, 15+29, s)-Nets in Base 7

(15, 15+29, 23)-Net over F₇ — Constructive and digital

Digital (15, 44, 23)-net over F₇, using

net from sequence [i] based on digital (15, 22)-sequence over F₇, using
- Niederreiter sequence [i]

(15, 15+29, 48)-Net over F₇ — Digital

Digital (15, 44, 48)-net over F₇, using

t-expansion [i] based on digital (13, 44, 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]

(15, 15+29, 388)-Net in Base 7 — Upper bound on s

There is no (15, 44, 389)-net in base 7, because

1 times m-reduction [i] would yield (15, 43, 389)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 2 231219 769864 192382 601217 480021 850201 > 7⁴³ [i]