MinT - Best Known (28, 28+31, s)-Nets in Base 8

Best Known (28, 28+31, s)-Nets in Base 8

(28, 28+31, 70)-Net over F₈ — Constructive and digital

Digital (28, 59, 70)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (4, 19, 25)-net over F₈, using
  - net from sequence [i] based on digital (4, 24)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, using
      - a function field by SÃ©mirat [i]
2. digital (9, 40, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(28, 28+31, 97)-Net over F₈ — Digital

Digital (28, 59, 97)-net over F₈, using

net from sequence [i] based on digital (28, 96)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
  - a curve from the manYPoints database [i]

(28, 28+31, 2839)-Net in Base 8 — Upper bound on s

There is no (28, 59, 2840)-net in base 8, because

1 times m-reduction [i] would yield (28, 58, 2840)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 24024 986416 473915 094259 638503 246309 242406 207338 777686 > 8⁵⁸ [i]