MinT - Best Known (71−60, 71, s)-Nets in Base 7

Best Known (71−60, 71, s)-Nets in Base 7

(71−60, 71, 19)-Net over F₇ — Constructive and digital

Digital (11, 71, 19)-net over F₇, using

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

(71−60, 71, 38)-Net over F₇ — Digital

Digital (11, 71, 38)-net over F₇, using

t-expansion [i] based on digital (9, 71, 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]

(71−60, 71, 90)-Net in Base 7 — Upper bound on s

There is no (11, 71, 91)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁷¹, 91, S₇, 60), but
- the linear programming bound shows that MÂ â‰¥ 1 437083 387944 628313 546760 786062 751076 565112 575733 385455 451782 844099 161276 329749 / 1 368795 020924 096645 > 7⁷¹ [i]