MinT - Best Known (147−95, 147, s)-Nets in Base 8

Best Known (147−95, 147, s)-Nets in Base 8

(147−95, 147, 98)-Net over F₈ — Constructive and digital

Digital (52, 147, 98)-net over F₈, using

t-expansion [i] based on digital (37, 147, 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]

(147−95, 147, 144)-Net over F₈ — Digital

Digital (52, 147, 144)-net over F₈, using

t-expansion [i] based on digital (45, 147, 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]

(147−95, 147, 1646)-Net in Base 8 — Upper bound on s

There is no (52, 147, 1647)-net in base 8, because

1 times m-reduction [i] would yield (52, 146, 1647)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 715453 216693 403108 174799 984835 132780 988392 369889 948317 557940 446981 958085 542676 454942 233378 204707 096230 356288 621117 065320 931234 154888 > 8¹⁴⁶ [i]