MinT - Best Known (63, 164, s)-Nets in Base 8

Best Known (63, 164, s)-Nets in Base 8

(63, 164, 98)-Net over F₈ — Constructive and digital

Digital (63, 164, 98)-net over F₈, using

t-expansion [i] based on digital (37, 164, 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]

(63, 164, 144)-Net over F₈ — Digital

Digital (63, 164, 144)-net over F₈, using

t-expansion [i] based on digital (45, 164, 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]

(63, 164, 2415)-Net in Base 8 — Upper bound on s

There is no (63, 164, 2416)-net in base 8, because

1 times m-reduction [i] would yield (63, 163, 2416)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1614 853712 870473 355727 488485 552680 676504 675036 566676 576026 338660 277343 287306 305677 250004 587861 690256 745024 701500 965137 823018 877566 697666 277018 806916 > 8¹⁶³ [i]