MinT - Best Known (60, 159, s)-Nets in Base 8

Best Known (60, 159, s)-Nets in Base 8

(60, 159, 98)-Net over F₈ — Constructive and digital

Digital (60, 159, 98)-net over F₈, using

t-expansion [i] based on digital (37, 159, 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]

(60, 159, 144)-Net over F₈ — Digital

Digital (60, 159, 144)-net over F₈, using

t-expansion [i] based on digital (45, 159, 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]

(60, 159, 2198)-Net in Base 8 — Upper bound on s

There is no (60, 159, 2199)-net in base 8, because

1 times m-reduction [i] would yield (60, 158, 2199)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 49135 463151 419166 044169 558649 735563 109348 969971 417311 235761 459697 424033 088934 478808 615697 203477 294162 268688 070789 415002 458126 966252 620866 004776 > 8¹⁵⁸ [i]