MinT - Best Known (33, 33+117, s)-Nets in Base 8

Best Known (33, 33+117, s)-Nets in Base 8

(33, 33+117, 65)-Net over F₈ — Constructive and digital

Digital (33, 150, 65)-net over F₈, using

t-expansion [i] based on digital (14, 150, 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]

(33, 33+117, 97)-Net over F₈ — Digital

Digital (33, 150, 97)-net over F₈, using

t-expansion [i] based on digital (28, 150, 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]

(33, 33+117, 633)-Net in Base 8 — Upper bound on s

There is no (33, 150, 634)-net in base 8, because

1 times m-reduction [i] would yield (33, 149, 634)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 366 360356 581591 899645 015279 146323 596682 142863 328998 967438 520745 189688 511541 953963 846473 789931 602010 257378 425156 654569 054952 836954 632880 > 8¹⁴⁹ [i]