MinT - Best Known (110−82, 110, s)-Nets in Base 8

Best Known (110−82, 110, s)-Nets in Base 8

(110−82, 110, 65)-Net over F₈ — Constructive and digital

Digital (28, 110, 65)-net over F₈, using

t-expansion [i] based on digital (14, 110, 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]

(110−82, 110, 97)-Net over F₈ — Digital

Digital (28, 110, 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]

(110−82, 110, 585)-Net in Base 8 — Upper bound on s

There is no (28, 110, 586)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2331 874636 503275 714460 718947 954583 567651 701912 799470 428354 853713 176618 817130 343992 494627 164665 036802 > 8¹¹⁰ [i]