MinT - Best Known (11, 44, s)-Nets in Base 7

Best Known (11, 44, s)-Nets in Base 7

(11, 44, 19)-Net over F₇ — Constructive and digital

Digital (11, 44, 19)-net over F₇, using

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

(11, 44, 38)-Net over F₇ — Digital

Digital (11, 44, 38)-net over F₇, using

t-expansion [i] based on digital (9, 44, 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]

(11, 44, 201)-Net in Base 7 — Upper bound on s

There is no (11, 44, 202)-net in base 7, because

1 times m-reduction [i] would yield (11, 43, 202)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 2 246408 610778 589155 876730 930678 684449 > 7⁴³ [i]