MinT - Best Known (52−37, 52, s)-Nets in Base 7

Best Known (52−37, 52, s)-Nets in Base 7

(52−37, 52, 23)-Net over F₇ — Constructive and digital

Digital (15, 52, 23)-net over F₇, using

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

(52−37, 52, 48)-Net over F₇ — Digital

Digital (15, 52, 48)-net over F₇, using

t-expansion [i] based on 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]

(52−37, 52, 300)-Net in Base 7 — Upper bound on s

There is no (15, 52, 301)-net in base 7, because

1 times m-reduction [i] would yield (15, 51, 301)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 12 713742 708272 967887 585997 307378 896372 044329 > 7⁵¹ [i]