MinT - Best Known (161−101, 161, s)-Nets in Base 8

Best Known (161−101, 161, s)-Nets in Base 8

(161−101, 161, 98)-Net over F₈ — Constructive and digital

Digital (60, 161, 98)-net over F₈, using

t-expansion [i] based on digital (37, 161, 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]

(161−101, 161, 144)-Net over F₈ — Digital

Digital (60, 161, 144)-net over F₈, using

t-expansion [i] based on digital (45, 161, 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]

(161−101, 161, 2128)-Net in Base 8 — Upper bound on s

There is no (60, 161, 2129)-net in base 8, because

1 times m-reduction [i] would yield (60, 160, 2129)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 159151 286987 590241 363745 099705 444191 772889 100658 374346 642633 494758 417608 042843 621241 369631 582269 931039 890698 738769 668272 391670 700751 596402 339424 > 8¹⁶⁰ [i]