MinT - Best Known (132−97, 132, s)-Nets in Base 8

Best Known (132−97, 132, s)-Nets in Base 8

(132−97, 132, 65)-Net over F₈ — Constructive and digital

Digital (35, 132, 65)-net over F₈, using

t-expansion [i] based on digital (14, 132, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(132−97, 132, 112)-Net over F₈ — Digital

Digital (35, 132, 112)-net over F₈, using

net from sequence [i] based on digital (35, 111)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(132−97, 132, 750)-Net in Base 8 — Upper bound on s

There is no (35, 132, 751)-net in base 8, because

1 times m-reduction [i] would yield (35, 131, 751)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 20804 609993 146775 771486 543108 924221 002697 615704 600477 981798 118588 092475 021803 674782 499664 908472 741112 744383 997276 120236 > 8¹³¹ [i]