MinT - Best Known (40, 163, s)-Nets in Base 8

Best Known (40, 163, s)-Nets in Base 8

(40, 163, 98)-Net over F₈ — Constructive and digital

Digital (40, 163, 98)-net over F₈, using

t-expansion [i] based on digital (37, 163, 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]

(40, 163, 129)-Net over F₈ — Digital

Digital (40, 163, 129)-net over F₈, using

t-expansion [i] based on digital (38, 163, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(40, 163, 804)-Net in Base 8 — Upper bound on s

There is no (40, 163, 805)-net in base 8, because

1 times m-reduction [i] would yield (40, 162, 805)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 212 232811 385702 945763 960701 901102 307636 520921 494957 133539 046731 643342 081640 378356 255541 747135 739832 252945 639777 152507 442742 228641 706315 753978 354688 > 8¹⁶² [i]