MinT - Best Known (127−89, 127, s)-Nets in Base 8

Best Known (127−89, 127, s)-Nets in Base 8

(127−89, 127, 98)-Net over F₈ — Constructive and digital

Digital (38, 127, 98)-net over F₈, using

t-expansion [i] based on digital (37, 127, 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]

(127−89, 127, 129)-Net over F₈ — Digital

Digital (38, 127, 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]

(127−89, 127, 922)-Net in Base 8 — Upper bound on s

There is no (38, 127, 923)-net in base 8, because

1 times m-reduction [i] would yield (38, 126, 923)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 617220 287410 640134 850165 930478 816003 841063 309700 037207 063292 817065 796187 655101 147495 348349 997457 072385 304910 969360 > 8¹²⁶ [i]