MinT - Best Known (26, 26+121, s)-Nets in Base 8

Best Known (26, 26+121, s)-Nets in Base 8

(26, 26+121, 65)-Net over F₈ — Constructive and digital

Digital (26, 147, 65)-net over F₈, using

t-expansion [i] based on digital (14, 147, 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]

(26, 26+121, 86)-Net over F₈ — Digital

Digital (26, 147, 86)-net over F₈, using

t-expansion [i] based on digital (25, 147, 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]

(26, 26+121, 484)-Net in Base 8 — Upper bound on s

There is no (26, 147, 485)-net in base 8, because

1 times m-reduction [i] would yield (26, 146, 485)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 722267 536880 103543 697995 244238 272585 460714 246282 029381 303993 457660 321314 840475 848680 784351 538499 262071 190280 179642 043685 062918 988136 > 8¹⁴⁶ [i]