MinT - Best Known (84−74, 84, s)-Nets in Base 7

Best Known (84−74, 84, s)-Nets in Base 7

(84−74, 84, 18)-Net over F₇ — Constructive and digital

Digital (10, 84, 18)-net over F₇, using

net from sequence [i] based on digital (10, 17)-sequence over F₇, using
- Niederreiter sequence [i]

(84−74, 84, 38)-Net over F₇ — Digital

Digital (10, 84, 38)-net over F₇, using

t-expansion [i] based on digital (9, 84, 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]

(84−74, 84, 78)-Net in Base 7 — Upper bound on s

There is no (10, 84, 79)-net in base 7, because

13 times m-reduction [i] would yield (10, 71, 79)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(7⁷¹, 79, S₇, 61), but
  - the linear programming bound shows that MÂ â‰¥ 6 065840 556126 502819 220899 224381 325317 379733 680091 354234 644732 726645 / 5 155114 > 7⁷¹ [i]