MinT - Best Known (15−9, 15, s)-Nets in Base 8

Best Known (15−9, 15, s)-Nets in Base 8

(15−9, 15, 28)-Net over F₈ — Constructive and digital

Digital (6, 15, 28)-net over F₈, using

t-expansion [i] based on digital (5, 15, 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]

(15−9, 15, 33)-Net in Base 8 — Constructive

(6, 15, 33)-net in base 8, using

1 times m-reduction [i] based on (6, 16, 33)-net in base 8, using
- base change [i] based on digital (2, 12, 33)-net over F₁₆, using
  - net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
      - a function field by SÃ©mirat [i]

(15−9, 15, 33)-Net over F₈ — Digital

Digital (6, 15, 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]

(15−9, 15, 455)-Net in Base 8 — Upper bound on s

There is no (6, 15, 456)-net in base 8, because

1 times m-reduction [i] would yield (6, 14, 456)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4 404539 061651 > 8¹⁴ [i]