MinT - Best Known (6, 6+38, s)-Nets in Base 7

Best Known (6, 6+38, s)-Nets in Base 7

(6, 6+38, 14)-Net over F₇ — Constructive and digital

Digital (6, 44, 14)-net over F₇, using

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

(6, 6+38, 24)-Net over F₇ — Digital

Digital (6, 44, 24)-net over F₇, using

t-expansion [i] based on digital (4, 44, 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+38, 55)-Net in Base 7 — Upper bound on s

There is no (6, 44, 56)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁴⁴, 56, S₇, 38), but
- the linear programming bound shows that MÂ â‰¥ 6357 573925 758601 938302 691003 913710 449603 165215 / 397 957131 > 7⁴⁴ [i]