MinT - Best Known (36, 117, s)-Nets in Base 8

Best Known (36, 117, s)-Nets in Base 8

(36, 117, 65)-Net over F₈ — Constructive and digital

Digital (36, 117, 65)-net over F₈, using

t-expansion [i] based on digital (14, 117, 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, 117, 112)-Net over F₈ — Digital

Digital (36, 117, 112)-net over F₈, using

t-expansion [i] based on digital (35, 117, 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, 117, 911)-Net in Base 8 — Upper bound on s

There is no (36, 117, 912)-net in base 8, because

1 times m-reduction [i] would yield (36, 116, 912)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 578 146360 640360 185702 209179 851714 398002 440912 420198 482563 297798 112023 108808 615298 867332 817133 674231 753180 > 8¹¹⁶ [i]