MinT - Best Known (59, 158, s)-Nets in Base 8

Best Known (59, 158, s)-Nets in Base 8

(59, 158, 98)-Net over F₈ — Constructive and digital

Digital (59, 158, 98)-net over F₈, using

t-expansion [i] based on digital (37, 158, 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]

(59, 158, 144)-Net over F₈ — Digital

Digital (59, 158, 144)-net over F₈, using

t-expansion [i] based on digital (45, 158, 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]

(59, 158, 2106)-Net in Base 8 — Upper bound on s

There is no (59, 158, 2107)-net in base 8, because

1 times m-reduction [i] would yield (59, 157, 2107)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6233 403186 975187 583517 077490 512380 346844 738974 410222 756651 911571 892424 916838 318704 331243 914860 826523 690561 317881 390760 209017 730183 089145 544874 > 8¹⁵⁷ [i]