MinT - Best Known (149−123, 149, s)-Nets in Base 8

Best Known (149−123, 149, s)-Nets in Base 8

(149−123, 149, 65)-Net over F₈ — Constructive and digital

Digital (26, 149, 65)-net over F₈, using

t-expansion [i] based on digital (14, 149, 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]

(149−123, 149, 86)-Net over F₈ — Digital

Digital (26, 149, 86)-net over F₈, using

t-expansion [i] based on digital (25, 149, 86)-net over F₈, using
- net from sequence [i] based on digital (25, 85)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 25 and N(F) ≥ 86, using
    - a curve from the manYPoints database [i]

(149−123, 149, 484)-Net in Base 8 — Upper bound on s

There is no (26, 149, 485)-net in base 8, because

1 times m-reduction [i] would yield (26, 148, 485)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 46 517023 065793 659408 601917 525243 566434 084230 805636 773946 481979 571532 975906 035727 045682 092438 320290 133802 100546 626135 968313 365169 569536 > 8¹⁴⁸ [i]