MinT - Best Known (152−105, 152, s)-Nets in Base 8

Best Known (152−105, 152, s)-Nets in Base 8

(152−105, 152, 98)-Net over F₈ — Constructive and digital

Digital (47, 152, 98)-net over F₈, using

t-expansion [i] based on digital (37, 152, 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]

(152−105, 152, 144)-Net over F₈ — Digital

Digital (47, 152, 144)-net over F₈, using

t-expansion [i] based on digital (45, 152, 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]

(152−105, 152, 1178)-Net in Base 8 — Upper bound on s

There is no (47, 152, 1179)-net in base 8, because

1 times m-reduction [i] would yield (47, 151, 1179)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23672 841774 179332 952897 437485 747023 379320 870965 174191 101723 804654 785627 502567 185244 824530 432045 827513 040585 920480 055818 890566 182556 080664 > 8¹⁵¹ [i]