MinT - Best Known (147−103, 147, s)-Nets in Base 8

Best Known (147−103, 147, s)-Nets in Base 8

(147−103, 147, 98)-Net over F₈ — Constructive and digital

Digital (44, 147, 98)-net over F₈, using

t-expansion [i] based on digital (37, 147, 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]

(147−103, 147, 130)-Net over F₈ — Digital

Digital (44, 147, 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]

(147−103, 147, 1059)-Net in Base 8 — Upper bound on s

There is no (44, 147, 1060)-net in base 8, because

1 times m-reduction [i] would yield (44, 146, 1060)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 722268 147419 434126 347931 907248 157190 765433 315400 672294 134088 259957 433202 351099 528164 656115 225468 821069 427725 961606 936496 352185 918912 > 8¹⁴⁶ [i]