MinT - Best Known (38−27, 38, s)-Nets in Base 7

Best Known (38−27, 38, s)-Nets in Base 7

(38−27, 38, 19)-Net over F₇ — Constructive and digital

Digital (11, 38, 19)-net over F₇, using

net from sequence [i] based on digital (11, 18)-sequence over F₇, using
- Niederreiter sequence [i]

(38−27, 38, 38)-Net over F₇ — Digital

Digital (11, 38, 38)-net over F₇, using

t-expansion [i] based on digital (9, 38, 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]

(38−27, 38, 232)-Net in Base 7 — Upper bound on s

There is no (11, 38, 233)-net in base 7, because

1 times m-reduction [i] would yield (11, 37, 233)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 19 484383 898194 865283 793039 660759 > 7³⁷ [i]