MinT - Best Known (36, 36+95, s)-Nets in Base 8

Best Known (36, 36+95, s)-Nets in Base 8

(36, 36+95, 65)-Net over F₈ — Constructive and digital

Digital (36, 131, 65)-net over F₈, using

t-expansion [i] based on digital (14, 131, 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]

(36, 36+95, 112)-Net over F₈ — Digital

Digital (36, 131, 112)-net over F₈, using

t-expansion [i] based on digital (35, 131, 112)-net over F₈, using
- net from sequence [i] based on digital (35, 111)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
    - a curve from the manYPoints database [i]

(36, 36+95, 796)-Net in Base 8 — Upper bound on s

There is no (36, 131, 797)-net in base 8, because

1 times m-reduction [i] would yield (36, 130, 797)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2598 615973 443880 984374 435061 641080 269477 672658 210515 138872 538510 942362 990222 784449 730777 578698 054719 279662 461899 384960 > 8¹³⁰ [i]