MinT - Best Known (10, 10+21, s)-Nets in Base 7

Best Known (10, 10+21, s)-Nets in Base 7

(10, 10+21, 18)-Net over F₇ — Constructive and digital

Digital (10, 31, 18)-net over F₇, using

net from sequence [i] based on digital (10, 17)-sequence over F₇, using
- Niederreiter sequence [i]

(10, 10+21, 38)-Net over F₇ — Digital

Digital (10, 31, 38)-net over F₇, using

t-expansion [i] based on digital (9, 31, 38)-net over F₇, using
- net from sequence [i] based on digital (9, 37)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 9 and N(F) ≥ 38, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(10, 10+21, 252)-Net in Base 7 — Upper bound on s

There is no (10, 31, 253)-net in base 7, because

1 times m-reduction [i] would yield (10, 30, 253)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 22 736091 442627 228872 544009 > 7³⁰ [i]