MinT - Best Known (10, 10+33, s)-Nets in Base 7

Best Known (10, 10+33, s)-Nets in Base 7

(10, 10+33, 18)-Net over F₇ — Constructive and digital

Digital (10, 43, 18)-net over F₇, using

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

(10, 10+33, 38)-Net over F₇ — Digital

Digital (10, 43, 38)-net over F₇, using

t-expansion [i] based on digital (9, 43, 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+33, 177)-Net in Base 7 — Upper bound on s

There is no (10, 43, 178)-net in base 7, because

1 times m-reduction [i] would yield (10, 42, 178)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 328061 123461 886812 784982 416737 414177 > 7⁴² [i]