MinT - Best Known (16, 16+27, s)-Nets in Base 7

Best Known (16, 16+27, s)-Nets in Base 7

(16, 16+27, 24)-Net over F₇ — Constructive and digital

Digital (16, 43, 24)-net over F₇, using

net from sequence [i] based on digital (16, 23)-sequence over F₇, using
- Niederreiter sequence [i]

(16, 16+27, 48)-Net over F₇ — Digital

Digital (16, 43, 48)-net over F₇, using

t-expansion [i] based on digital (13, 43, 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]

(16, 16+27, 499)-Net in Base 7 — Upper bound on s

There is no (16, 43, 500)-net in base 7, because

1 times m-reduction [i] would yield (16, 42, 500)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 315707 319882 084739 028368 261437 111001 > 7⁴² [i]