MinT - Best Known (122−98, 122, s)-Nets in Base 8

Best Known (122−98, 122, s)-Nets in Base 8

(122−98, 122, 65)-Net over F₈ — Constructive and digital

Digital (24, 122, 65)-net over F₈, using

t-expansion [i] based on digital (14, 122, 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]

(122−98, 122, 81)-Net over F₈ — Digital

Digital (24, 122, 81)-net over F₈, using

net from sequence [i] based on digital (24, 80)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 24 and N(F) ≥ 81, using
  - a curve from the manYPoints database [i]

(122−98, 122, 453)-Net in Base 8 — Upper bound on s

There is no (24, 122, 454)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 158 951258 931346 571854 811317 990539 981980 520905 529750 309020 428999 494731 322789 880750 972896 673058 708829 966634 500492 > 8¹²² [i]