MinT - Best Known (55−30, 55, s)-Nets in Base 7

Best Known (55−30, 55, s)-Nets in Base 7

(55−30, 55, 31)-Net over F₇ — Constructive and digital

Digital (25, 55, 31)-net over F₇, using

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

(55−30, 55, 72)-Net over F₇ — Digital

Digital (25, 55, 72)-net over F₇, using

t-expansion [i] based on digital (22, 55, 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]

(55−30, 55, 1334)-Net in Base 7 — Upper bound on s

There is no (25, 55, 1335)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 30484 167785 103284 715896 888232 216704 934498 721255 > 7⁵⁵ [i]