MinT - Best Known (170−129, 170, s)-Nets in Base 8

Best Known (170−129, 170, s)-Nets in Base 8

(170−129, 170, 98)-Net over F₈ — Constructive and digital

Digital (41, 170, 98)-net over F₈, using

t-expansion [i] based on digital (37, 170, 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]

(170−129, 170, 129)-Net over F₈ — Digital

Digital (41, 170, 129)-net over F₈, using

t-expansion [i] based on digital (38, 170, 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]

(170−129, 170, 814)-Net in Base 8 — Upper bound on s

There is no (41, 170, 815)-net in base 8, because

1 times m-reduction [i] would yield (41, 169, 815)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 427 523239 389749 212297 394213 131218 371494 241195 847569 213596 352674 194576 579581 664503 988672 242770 716863 785989 183496 068403 590283 229145 327258 350145 300927 630204 > 8¹⁶⁹ [i]