MinT - Best Known (127−104, 127, s)-Nets in Base 8

Best Known (127−104, 127, s)-Nets in Base 8

(127−104, 127, 65)-Net over F₈ — Constructive and digital

Digital (23, 127, 65)-net over F₈, using

t-expansion [i] based on digital (14, 127, 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]

(127−104, 127, 76)-Net over F₈ — Digital

Digital (23, 127, 76)-net over F₈, using

t-expansion [i] based on digital (20, 127, 76)-net over F₈, using
- net from sequence [i] based on digital (20, 75)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 20 and N(F) ≥ 76, using
    - a curve from the manYPoints database [i]

(127−104, 127, 431)-Net in Base 8 — Upper bound on s

There is no (23, 127, 432)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 117489 019012 451441 878847 793814 767675 129611 482493 469072 364196 910158 588105 696998 682480 701749 745255 715807 965227 301512 > 8¹²⁷ [i]