MinT - Best Known (6, 6+21, s)-Nets in Base 7

Best Known (6, 6+21, s)-Nets in Base 7

(6, 6+21, 14)-Net over F₇ — Constructive and digital

Digital (6, 27, 14)-net over F₇, using

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

(6, 6+21, 24)-Net over F₇ — Digital

Digital (6, 27, 24)-net over F₇, using

t-expansion [i] based on digital (4, 27, 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]

(6, 6+21, 112)-Net in Base 7 — Upper bound on s

There is no (6, 27, 113)-net in base 7, because

1 times m-reduction [i] would yield (6, 26, 113)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 9537 433002 454176 487633 > 7²⁶ [i]