MinT - Best Known (163−130, 163, s)-Nets in Base 8

Best Known (163−130, 163, s)-Nets in Base 8

(163−130, 163, 65)-Net over F₈ — Constructive and digital

Digital (33, 163, 65)-net over F₈, using

t-expansion [i] based on digital (14, 163, 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]

(163−130, 163, 97)-Net over F₈ — Digital

Digital (33, 163, 97)-net over F₈, using

t-expansion [i] based on digital (28, 163, 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]

(163−130, 163, 617)-Net in Base 8 — Upper bound on s

There is no (33, 163, 618)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1667 801959 471077 876246 691573 101600 851850 151276 107655 989588 328347 829121 054813 970137 772644 467271 086429 224611 230510 978459 327978 575117 382929 228244 202585 > 8¹⁶³ [i]