MinT - Best Known (22, 22+57, s)-Nets in Base 7

Best Known (22, 22+57, s)-Nets in Base 7

(22, 22+57, 29)-Net over F₇ — Constructive and digital

Digital (22, 79, 29)-net over F₇, using

t-expansion [i] based on digital (21, 79, 29)-net over F₇, using
- net from sequence [i] based on digital (21, 28)-sequence over F₇, using
  - Niederreiter sequence [i]

(22, 22+57, 72)-Net over F₇ — Digital

Digital (22, 79, 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]

(22, 22+57, 407)-Net in Base 7 — Upper bound on s

There is no (22, 79, 408)-net in base 7, because

1 times m-reduction [i] would yield (22, 78, 408)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 842047 556202 790988 920158 395889 967523 435935 340516 173055 373894 992449 > 7⁷⁸ [i]