MinT - Best Known (137−107, 137, s)-Nets in Base 8

Best Known (137−107, 137, s)-Nets in Base 8

(137−107, 137, 65)-Net over F₈ — Constructive and digital

Digital (30, 137, 65)-net over F₈, using

t-expansion [i] based on digital (14, 137, 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]

(137−107, 137, 97)-Net over F₈ — Digital

Digital (30, 137, 97)-net over F₈, using

t-expansion [i] based on digital (28, 137, 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]

(137−107, 137, 577)-Net in Base 8 — Upper bound on s

There is no (30, 137, 578)-net in base 8, because

1 times m-reduction [i] would yield (30, 136, 578)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 661 258726 398858 871366 577706 894058 512854 246466 148043 930493 098729 166290 981929 084258 338835 898075 265833 974279 805027 755113 546992 > 8¹³⁶ [i]