MinT - Best Known (96−72, 96, s)-Nets in Base 7

Best Known (96−72, 96, s)-Nets in Base 7

(96−72, 96, 30)-Net over F₇ — Constructive and digital

Digital (24, 96, 30)-net over F₇, using

t-expansion [i] based on digital (23, 96, 30)-net over F₇, using
- net from sequence [i] based on digital (23, 29)-sequence over F₇, using
  - Niederreiter sequence [i]

(96−72, 96, 72)-Net over F₇ — Digital

Digital (24, 96, 72)-net over F₇, using

t-expansion [i] based on digital (22, 96, 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]

(96−72, 96, 403)-Net in Base 7 — Upper bound on s

There is no (24, 96, 404)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1386 266996 736020 129574 996911 448720 138870 645040 509040 906877 312118 919983 911912 953345 > 7⁹⁶ [i]