MinT - Best Known (5, 5+26, s)-Nets in Base 8

Best Known (5, 5+26, s)-Nets in Base 8

(5, 5+26, 28)-Net over F₈ — Constructive and digital

Digital (5, 31, 28)-net over F₈, using

net from sequence [i] based on digital (5, 27)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
  - a function field by SÃ©mirat [i]

(5, 5+26, 29)-Net over F₈ — Digital

Digital (5, 31, 29)-net over F₈, using

net from sequence [i] based on digital (5, 28)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 29, using
  - a curve from the manYPoints database [i]

(5, 5+26, 106)-Net in Base 8 — Upper bound on s

There is no (5, 31, 107)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8³¹, 107, S₈, 26), but
- the linear programming bound shows that MÂ â‰¥ 65368 242321 161129 025024 659814 054385 090063 424739 606528 / 6 409905 634971 784499 166839 > 8³¹ [i]