MinT - Best Known (88−49, 88, s)-Nets in Base 8

Best Known (88−49, 88, s)-Nets in Base 8

(88−49, 88, 98)-Net over F₈ — Constructive and digital

Digital (39, 88, 98)-net over F₈, using

t-expansion [i] based on digital (37, 88, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(88−49, 88, 129)-Net over F₈ — Digital

Digital (39, 88, 129)-net over F₈, using

t-expansion [i] based on digital (38, 88, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(88−49, 88, 2615)-Net in Base 8 — Upper bound on s

There is no (39, 88, 2616)-net in base 8, because

1 times m-reduction [i] would yield (39, 87, 2616)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 733885 315439 195256 316480 071699 021808 495807 840162 372884 866313 941032 545471 682868 > 8⁸⁷ [i]