MinT - Best Known (169−125, 169, s)-Nets in Base 8

Best Known (169−125, 169, s)-Nets in Base 8

(169−125, 169, 98)-Net over F₈ — Constructive and digital

Digital (44, 169, 98)-net over F₈, using

t-expansion [i] based on digital (37, 169, 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]

(169−125, 169, 130)-Net over F₈ — Digital

Digital (44, 169, 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]

(169−125, 169, 918)-Net in Base 8 — Upper bound on s

There is no (44, 169, 919)-net in base 8, because

1 times m-reduction [i] would yield (44, 168, 919)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 54 872968 266230 723345 407926 421534 437712 563403 175129 262338 924377 808402 204714 344620 328981 791335 048211 260134 383626 402022 162646 228411 015982 034227 327666 909744 > 8¹⁶⁸ [i]