MinT - Best Known (81−69, 81, s)-Nets in Base 7

Best Known (81−69, 81, s)-Nets in Base 7

(81−69, 81, 20)-Net over F₇ — Constructive and digital

Digital (12, 81, 20)-net over F₇, using

net from sequence [i] based on digital (12, 19)-sequence over F₇, using
- Niederreiter sequence [i]

(81−69, 81, 38)-Net over F₇ — Digital

Digital (12, 81, 38)-net over F₇, using

t-expansion [i] based on digital (9, 81, 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]

(81−69, 81, 91)-Net in Base 7 — Upper bound on s

There is no (12, 81, 92)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁸¹, 92, S₇, 69), but
- the linear programming bound shows that MÂ â‰¥ 864 559770 761790 045338 407853 839994 667208 992212 813032 556141 743602 440684 512083 / 2 553125 > 7⁸¹ [i]