MinT - Best Known (49−34, 49, s)-Nets in Base 7

Best Known (49−34, 49, s)-Nets in Base 7

(49−34, 49, 23)-Net over F₇ — Constructive and digital

Digital (15, 49, 23)-net over F₇, using

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

(49−34, 49, 48)-Net over F₇ — Digital

Digital (15, 49, 48)-net over F₇, using

t-expansion [i] based on digital (13, 49, 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]

(49−34, 49, 315)-Net in Base 7 — Upper bound on s

There is no (15, 49, 316)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 262076 641388 122360 160697 883499 756499 200617 > 7⁴⁹ [i]