MinT - Best Known (82−58, 82, s)-Nets in Base 7

Best Known (82−58, 82, s)-Nets in Base 7

(82−58, 82, 30)-Net over F₇ — Constructive and digital

Digital (24, 82, 30)-net over F₇, using

t-expansion [i] based on digital (23, 82, 30)-net over F₇, using
- net from sequence [i] based on digital (23, 29)-sequence over F₇, using
  - Niederreiter sequence [i]

(82−58, 82, 72)-Net over F₇ — Digital

Digital (24, 82, 72)-net over F₇, using

t-expansion [i] based on digital (22, 82, 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]

(82−58, 82, 458)-Net in Base 7 — Upper bound on s

There is no (24, 82, 459)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 2054 377264 185073 724758 805068 742859 517751 268977 608844 741859 841865 313115 > 7⁸² [i]