MinT - Best Known (166−133, 166, s)-Nets in Base 8

Best Known (166−133, 166, s)-Nets in Base 8

(166−133, 166, 65)-Net over F₈ — Constructive and digital

Digital (33, 166, 65)-net over F₈, using

t-expansion [i] based on digital (14, 166, 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]

(166−133, 166, 97)-Net over F₈ — Digital

Digital (33, 166, 97)-net over F₈, using

t-expansion [i] based on digital (28, 166, 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]

(166−133, 166, 616)-Net in Base 8 — Upper bound on s

There is no (33, 166, 617)-net in base 8, because

1 times m-reduction [i] would yield (33, 165, 617)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 112118 801700 003369 365979 708600 917743 713580 531778 804858 985617 511585 803551 807532 141256 052030 228459 437124 680973 217584 930927 062987 351310 325361 535018 261620 > 8¹⁶⁵ [i]