MinT - Best Known (116−83, 116, s)-Nets in Base 8

Best Known (116−83, 116, s)-Nets in Base 8

(116−83, 116, 65)-Net over F₈ — Constructive and digital

Digital (33, 116, 65)-net over F₈, using

t-expansion [i] based on digital (14, 116, 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]

(116−83, 116, 97)-Net over F₈ — Digital

Digital (33, 116, 97)-net over F₈, using

t-expansion [i] based on digital (28, 116, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(116−83, 116, 761)-Net in Base 8 — Upper bound on s

There is no (33, 116, 762)-net in base 8, because

1 times m-reduction [i] would yield (33, 115, 762)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 74 673270 106234 318977 175998 228617 112699 560238 899617 957565 636485 309150 373266 707293 798517 657590 984444 412045 > 8¹¹⁵ [i]