MinT - Best Known (49−38, 49, s)-Nets in Base 7

Best Known (49−38, 49, s)-Nets in Base 7

(49−38, 49, 19)-Net over F₇ — Constructive and digital

Digital (11, 49, 19)-net over F₇, using

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

(49−38, 49, 38)-Net over F₇ — Digital

Digital (11, 49, 38)-net over F₇, using

t-expansion [i] based on digital (9, 49, 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]

(49−38, 49, 184)-Net in Base 7 — Upper bound on s

There is no (11, 49, 185)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁴⁹, 185, S₇, 38), but
- the linear programming bound shows that MÂ â‰¥ 541652 723760 274993 097537 055750 550577 682157 124385 190740 786080 047095 559544 423502 890625 / 2 107499 601470 151906 229902 495056 605345 802656 > 7⁴⁹ [i]