MinT - Best Known (6, 6+23, s)-Nets in Base 8

Best Known (6, 6+23, s)-Nets in Base 8

(6, 6+23, 28)-Net over F₈ — Constructive and digital

Digital (6, 29, 28)-net over F₈, using

t-expansion [i] based on digital (5, 29, 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]

(6, 6+23, 33)-Net over F₈ — Digital

Digital (6, 29, 33)-net over F₈, using

net from sequence [i] based on digital (6, 32)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 6 and N(F) ≥ 33, using
  - Drinfeld modules of rank 1 [i]

(6, 6+23, 133)-Net in Base 8 — Upper bound on s

There is no (6, 29, 134)-net in base 8, because

1 times m-reduction [i] would yield (6, 28, 134)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 20 819229 931871 392016 191904 > 8²⁸ [i]