MinT - Best Known (65, 65+90, s)-Nets in Base 8

Best Known (65, 65+90, s)-Nets in Base 8

(65, 65+90, 98)-Net over F₈ — Constructive and digital

Digital (65, 155, 98)-net over F₈, using

t-expansion [i] based on digital (37, 155, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(65, 65+90, 144)-Net over F₈ — Digital

Digital (65, 155, 144)-net over F₈, using

t-expansion [i] based on digital (45, 155, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(65, 65+90, 150)-Net in Base 8

(65, 155, 150)-net in base 8, using

1 times m-reduction [i] based on (65, 156, 150)-net in base 8, using
- base change [i] based on digital (26, 117, 150)-net over F₁₆, using
  - net from sequence [i] based on digital (26, 149)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 26 and N(F) ≥ 150, using
      - a curve from the manYPoints database [i]

(65, 65+90, 3220)-Net in Base 8 — Upper bound on s

There is no (65, 155, 3221)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 96 041982 185422 742307 206366 887409 429082 194145 449613 207185 565078 917066 200963 465573 218311 993938 245981 393249 794613 491192 456229 121159 744120 877824 > 8¹⁵⁵ [i]