MinT - Best Known (39, 39+109, s)-Nets in Base 8

Best Known (39, 39+109, s)-Nets in Base 8

(39, 39+109, 98)-Net over F₈ — Constructive and digital

Digital (39, 148, 98)-net over F₈, using

t-expansion [i] based on digital (37, 148, 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+109, 129)-Net over F₈ — Digital

Digital (39, 148, 129)-net over F₈, using

t-expansion [i] based on digital (38, 148, 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+109, 826)-Net in Base 8 — Upper bound on s

There is no (39, 148, 827)-net in base 8, because

1 times m-reduction [i] would yield (39, 147, 827)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 713883 138323 277992 704533 643743 600520 289124 471961 187285 391933 103725 983606 609830 063334 224366 893694 804803 443203 854409 944949 073866 841534 > 8¹⁴⁷ [i]