MinT - Best Known (55−48, 55, s)-Nets in Base 7

Best Known (55−48, 55, s)-Nets in Base 7

(55−48, 55, 15)-Net over F₇ — Constructive and digital

Digital (7, 55, 15)-net over F₇, using

net from sequence [i] based on digital (7, 14)-sequence over F₇, using
- Niederreiter sequence [i]

(55−48, 55, 32)-Net over F₇ — Digital

Digital (7, 55, 32)-net over F₇, using

net from sequence [i] based on digital (7, 31)-sequence over F₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 7 and N(F) ≥ 32, using
  - an algebraic function field over â„¤₇ by Yeo [i]

(55−48, 55, 59)-Net in Base 7 — Upper bound on s

There is no (7, 55, 60)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁵⁵, 60, S₇, 48), but
- the linear programming bound shows that MÂ â‰¥ 392948 425633 075727 327211 671891 403255 967254 645259 / 11 > 7⁵⁵ [i]