MinT - Best Known (99−76, 99, s)-Nets in Base 7

Best Known (99−76, 99, s)-Nets in Base 7

(99−76, 99, 30)-Net over F₇ — Constructive and digital

Digital (23, 99, 30)-net over F₇, using

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

(99−76, 99, 72)-Net over F₇ — Digital

Digital (23, 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]

(99−76, 99, 374)-Net in Base 7 — Upper bound on s

There is no (23, 99, 375)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 504441 790170 385213 359850 356316 409770 029184 309519 172928 482398 644126 457833 780698 780941 > 7⁹⁹ [i]