MinT - Best Known (28, 28+108, s)-Nets in Base 8

Best Known (28, 28+108, s)-Nets in Base 8

(28, 28+108, 65)-Net over F₈ — Constructive and digital

Digital (28, 136, 65)-net over F₈, using

t-expansion [i] based on digital (14, 136, 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]

(28, 28+108, 97)-Net over F₈ — Digital

Digital (28, 136, 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]

(28, 28+108, 529)-Net in Base 8 — Upper bound on s

There is no (28, 136, 530)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 667 422181 887591 686928 691657 239162 793970 479060 178604 716483 043983 186326 854980 781141 763029 889340 447027 513588 135359 366875 120896 > 8¹³⁶ [i]