MinT - Best Known (66, 66+95, s)-Nets in Base 8

Best Known (66, 66+95, s)-Nets in Base 8

(66, 66+95, 98)-Net over F₈ — Constructive and digital

Digital (66, 161, 98)-net over F₈, using

t-expansion [i] based on digital (37, 161, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(66, 66+95, 144)-Net over F₈ — Digital

Digital (66, 161, 144)-net over F₈, using

t-expansion [i] based on digital (45, 161, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(66, 66+95, 3084)-Net in Base 8 — Upper bound on s

There is no (66, 161, 3085)-net in base 8, because

1 times m-reduction [i] would yield (66, 160, 3085)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 140752 964367 731791 153263 722199 504107 212208 649325 797430 740501 636650 093205 170029 502754 720976 808196 168027 893014 081538 260342 038463 694175 876952 245248 > 8¹⁶⁰ [i]