MinT - Best Known (137−113, 137, s)-Nets in Base 8

Best Known (137−113, 137, s)-Nets in Base 8

(137−113, 137, 65)-Net over F₈ — Constructive and digital

Digital (24, 137, 65)-net over F₈, using

t-expansion [i] based on digital (14, 137, 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]

(137−113, 137, 81)-Net over F₈ — Digital

Digital (24, 137, 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]

(137−113, 137, 449)-Net in Base 8 — Upper bound on s

There is no (24, 137, 450)-net in base 8, because

1 times m-reduction [i] would yield (24, 136, 450)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 727 562503 483551 910239 267517 545865 558478 928723 488376 161742 397812 202464 122908 088320 987730 449764 170399 240294 421745 584804 847592 > 8¹³⁶ [i]