MinT - Best Known (43, 134, s)-Nets in Base 8

Best Known (43, 134, s)-Nets in Base 8

(43, 134, 98)-Net over F₈ — Constructive and digital

Digital (43, 134, 98)-net over F₈, using

t-expansion [i] based on digital (37, 134, 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]

(43, 134, 129)-Net over F₈ — Digital

Digital (43, 134, 129)-net over F₈, using

t-expansion [i] based on digital (38, 134, 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]

(43, 134, 1147)-Net in Base 8 — Upper bound on s

There is no (43, 134, 1148)-net in base 8, because

1 times m-reduction [i] would yield (43, 133, 1148)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 329263 580265 021509 676184 366584 531357 266493 820128 013551 296026 550926 884765 621435 797737 433229 876807 418500 557304 892572 098388 > 8¹³³ [i]