MinT - Best Known (73−47, 73, s)-Nets in Base 7

Best Known (73−47, 73, s)-Nets in Base 7

(73−47, 73, 31)-Net over F₇ — Constructive and digital

Digital (26, 73, 31)-net over F₇, using

t-expansion [i] based on digital (25, 73, 31)-net over F₇, using
- net from sequence [i] based on digital (25, 30)-sequence over F₇, using
  - Niederreiter sequence [i]

(73−47, 73, 72)-Net over F₇ — Digital

Digital (26, 73, 72)-net over F₇, using

t-expansion [i] based on digital (22, 73, 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]

(73−47, 73, 680)-Net in Base 7 — Upper bound on s

There is no (26, 73, 681)-net in base 7, because

1 times m-reduction [i] would yield (26, 72, 681)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 7 263549 584086 981182 954454 069737 455103 406601 666388 320577 579319 > 7⁷² [i]