MinT - Best Known (163−131, 163, s)-Nets in Base 8

Best Known (163−131, 163, s)-Nets in Base 8

(163−131, 163, 65)-Net over F₈ — Constructive and digital

Digital (32, 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]

(163−131, 163, 97)-Net over F₈ — Digital

Digital (32, 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]

(163−131, 163, 596)-Net in Base 8 — Upper bound on s

There is no (32, 163, 597)-net in base 8, because

1 times m-reduction [i] would yield (32, 162, 597)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 202 384697 845414 526410 387524 524272 464103 089906 527285 017447 311326 138240 642262 192249 046950 791355 688746 074874 715833 260505 142797 267324 325784 683657 432612 > 8¹⁶² [i]