MinT - Best Known (21−15, 21, s)-Nets in Base 7

Best Known (21−15, 21, s)-Nets in Base 7

(21−15, 21, 14)-Net over F₇ — Constructive and digital

Digital (6, 21, 14)-net over F₇, using

net from sequence [i] based on digital (6, 13)-sequence over F₇, using
- Niederreiter sequence [i]

(21−15, 21, 24)-Net over F₇ — Digital

Digital (6, 21, 24)-net over F₇, using

t-expansion [i] based on digital (4, 21, 24)-net over F₇, using
- net from sequence [i] based on digital (4, 23)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 4 and N(F) ≥ 24, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(21−15, 21, 142)-Net in Base 7 — Upper bound on s

There is no (6, 21, 143)-net in base 7, because

1 times m-reduction [i] would yield (6, 20, 143)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 82879 787041 865815 > 7²⁰ [i]