MinT - Best Known (39, 39+91, s)-Nets in Base 8

Best Known (39, 39+91, s)-Nets in Base 8

(39, 39+91, 98)-Net over F₈ — Constructive and digital

Digital (39, 130, 98)-net over F₈, using

t-expansion [i] based on digital (37, 130, 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]

(39, 39+91, 129)-Net over F₈ — Digital

Digital (39, 130, 129)-net over F₈, using

t-expansion [i] based on digital (38, 130, 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]

(39, 39+91, 948)-Net in Base 8 — Upper bound on s

There is no (39, 130, 949)-net in base 8, because

1 times m-reduction [i] would yield (39, 129, 949)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 316 558231 882941 526394 591060 710969 730497 760741 045518 288415 722634 524111 266839 708815 084166 386685 531624 028585 306512 315392 > 8¹²⁹ [i]