MinT - Best Known (145−95, 145, s)-Nets in Base 8

Best Known (145−95, 145, s)-Nets in Base 8

(145−95, 145, 98)-Net over F₈ — Constructive and digital

Digital (50, 145, 98)-net over F₈, using

t-expansion [i] based on digital (37, 145, 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]

(145−95, 145, 144)-Net over F₈ — Digital

Digital (50, 145, 144)-net over F₈, using

t-expansion [i] based on digital (45, 145, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(145−95, 145, 1504)-Net in Base 8 — Upper bound on s

There is no (50, 145, 1505)-net in base 8, because

1 times m-reduction [i] would yield (50, 144, 1505)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11166 735632 471501 034844 948054 839692 085607 588411 420944 089765 675544 336972 662674 464264 192208 329261 808257 477831 458167 696491 853789 025088 > 8¹⁴⁴ [i]