MinT - Best Known (76−65, 76, s)-Nets in Base 7

Best Known (76−65, 76, s)-Nets in Base 7

(76−65, 76, 19)-Net over F₇ — Constructive and digital

Digital (11, 76, 19)-net over F₇, using

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

(76−65, 76, 38)-Net over F₇ — Digital

Digital (11, 76, 38)-net over F₇, using

t-expansion [i] based on digital (9, 76, 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]

(76−65, 76, 85)-Net in Base 7 — Upper bound on s

There is no (11, 76, 86)-net in base 7, because

3 times m-reduction [i] would yield (11, 73, 86)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(7⁷³, 86, S₇, 62), but
  - the linear programming bound shows that MÂ â‰¥ 161806 475312 686849 725066 839632 058773 007336 398342 000423 616787 753916 743157 / 3278 044341 > 7⁷³ [i]