MinT - Best Known (153−111, 153, s)-Nets in Base 8

Best Known (153−111, 153, s)-Nets in Base 8

(153−111, 153, 98)-Net over F₈ — Constructive and digital

Digital (42, 153, 98)-net over F₈, using

t-expansion [i] based on digital (37, 153, 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]

(153−111, 153, 129)-Net over F₈ — Digital

Digital (42, 153, 129)-net over F₈, using

t-expansion [i] based on digital (38, 153, 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]

(153−111, 153, 920)-Net in Base 8 — Upper bound on s

There is no (42, 153, 921)-net in base 8, because

1 times m-reduction [i] would yield (42, 152, 921)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 194461 529923 803785 448016 772582 086205 501530 407271 995211 160223 052303 865930 065607 793376 369774 209265 329314 502243 263947 671864 574383 028570 935776 > 8¹⁵² [i]