MinT - Best Known (4, 4+26, s)-Nets in Base 9

Best Known (4, 4+26, s)-Nets in Base 9

(4, 4+26, 30)-Net over F₉ — Constructive and digital

Digital (4, 30, 30)-net over F₉, using

net from sequence [i] based on digital (4, 29)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
  - a function field by SÃ©mirat [i]

(4, 4+26, 99)-Net in Base 9 — Upper bound on s

There is no (4, 30, 100)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9³⁰, 100, S₉, 26), but
- the linear programming bound shows that MÂ â‰¥ 476487 515807 967156 235733 808831 100712 503587 578415 / 10 980434 953481 037263 > 9³⁰ [i]