MinT - Best Known (52, 52+73, s)-Nets in Base 8

Best Known (52, 52+73, s)-Nets in Base 8

(52, 52+73, 98)-Net over F₈ — Constructive and digital

Digital (52, 125, 98)-net over F₈, using

t-expansion [i] based on digital (37, 125, 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]

(52, 52+73, 144)-Net over F₈ — Digital

Digital (52, 125, 144)-net over F₈, using

t-expansion [i] based on digital (45, 125, 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]

(52, 52+73, 2609)-Net in Base 8 — Upper bound on s

There is no (52, 125, 2610)-net in base 8, because

1 times m-reduction [i] would yield (52, 124, 2610)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 9699 556969 578319 804307 889622 441651 797029 326487 245796 185377 148619 484343 479355 988596 526858 297631 481066 893130 221396 > 8¹²⁴ [i]