MinT - Best Known (149−81, 149, s)-Nets in Base 8

Best Known (149−81, 149, s)-Nets in Base 8

(149−81, 149, 130)-Net over F₈ — Constructive and digital

Digital (68, 149, 130)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (14, 54, 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]
2. digital (14, 95, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(149−81, 149, 173)-Net over F₈ — Digital

Digital (68, 149, 173)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−81, 149, 4919)-Net in Base 8 — Upper bound on s

There is no (68, 149, 4920)-net in base 8, because

1 times m-reduction [i] would yield (68, 148, 4920)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 45 660813 568251 466257 424546 366211 707943 465350 135154 194136 063807 021563 055410 761060 457014 768349 168924 818529 459066 035059 348228 202696 540270 > 8¹⁴⁸ [i]