MinT - Best Known (33−27, 33, s)-Nets in Base 7

Best Known (33−27, 33, s)-Nets in Base 7

(33−27, 33, 14)-Net over F₇ — Constructive and digital

Digital (6, 33, 14)-net over F₇, using

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

(33−27, 33, 24)-Net over F₇ — Digital

Digital (6, 33, 24)-net over F₇, using

t-expansion [i] based on digital (4, 33, 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]

(33−27, 33, 103)-Net in Base 7 — Upper bound on s

There is no (6, 33, 104)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7³³, 104, S₇, 27), but
- the linear programming bound shows that MÂ â‰¥ 37951 039866 179845 959716 713627 631631 055129 769140 396875 / 4 815422 861943 262060 590491 > 7³³ [i]