MinT - Best Known (78−52, 78, s)-Nets in Base 7

Best Known (78−52, 78, s)-Nets in Base 7

(78−52, 78, 31)-Net over F₇ — Constructive and digital

Digital (26, 78, 31)-net over F₇, using

t-expansion [i] based on digital (25, 78, 31)-net over F₇, using
- net from sequence [i] based on digital (25, 30)-sequence over F₇, using
  - Niederreiter sequence [i]

(78−52, 78, 72)-Net over F₇ — Digital

Digital (26, 78, 72)-net over F₇, using

t-expansion [i] based on digital (22, 78, 72)-net over F₇, using
- net from sequence [i] based on digital (22, 71)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 22 and N(F) ≥ 72, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(78−52, 78, 586)-Net in Base 7 — Upper bound on s

There is no (26, 78, 587)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 845984 341160 326497 730052 003542 322535 050060 452834 052733 760689 760765 > 7⁷⁸ [i]