MinT - Best Known (99−73, 99, s)-Nets in Base 7

Best Known (99−73, 99, s)-Nets in Base 7

(99−73, 99, 31)-Net over F₇ — Constructive and digital

Digital (26, 99, 31)-net over F₇, using

t-expansion [i] based on digital (25, 99, 31)-net over F₇, using
- net from sequence [i] based on digital (25, 30)-sequence over F₇, using
  - Niederreiter sequence [i]

(99−73, 99, 72)-Net over F₇ — Digital

Digital (26, 99, 72)-net over F₇, using

t-expansion [i] based on digital (22, 99, 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]

(99−73, 99, 452)-Net in Base 7 — Upper bound on s

There is no (26, 99, 453)-net in base 7, because

1 times m-reduction [i] would yield (26, 98, 453)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 69385 147609 536006 206572 036982 542294 432693 507216 855137 830991 950585 145824 942358 097825 > 7⁹⁸ [i]