MinT - Best Known (142−87, 142, s)-Nets in Base 8

Best Known (142−87, 142, s)-Nets in Base 8

(142−87, 142, 98)-Net over F₈ — Constructive and digital

Digital (55, 142, 98)-net over F₈, using

t-expansion [i] based on digital (37, 142, 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]

(142−87, 142, 144)-Net over F₈ — Digital

Digital (55, 142, 144)-net over F₈, using

t-expansion [i] based on digital (45, 142, 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]

(142−87, 142, 2179)-Net in Base 8 — Upper bound on s

There is no (55, 142, 2180)-net in base 8, because

1 times m-reduction [i] would yield (55, 141, 2180)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 21 974660 944941 997040 196534 384166 700700 212946 783395 894607 712079 465788 983161 995916 321401 456954 634980 874100 330772 406544 794086 290384 > 8¹⁴¹ [i]