MinT - Best Known (163−119, 163, s)-Nets in Base 8

Best Known (163−119, 163, s)-Nets in Base 8

(163−119, 163, 98)-Net over F₈ — Constructive and digital

Digital (44, 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]

(163−119, 163, 130)-Net over F₈ — Digital

Digital (44, 163, 130)-net over F₈, using

net from sequence [i] based on digital (44, 129)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 44 and N(F) ≥ 130, using
  - a curve from the manYPoints database [i]

(163−119, 163, 946)-Net in Base 8 — Upper bound on s

There is no (44, 163, 947)-net in base 8, because

1 times m-reduction [i] would yield (44, 162, 947)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 202 106093 535605 730823 529541 357881 278350 664389 181796 640786 230344 557379 912145 990147 651393 286904 598900 041028 160494 640471 771159 315508 702924 787572 144384 > 8¹⁶² [i]