MinT - Best Known (42, 42+131, s)-Nets in Base 8

Best Known (42, 42+131, s)-Nets in Base 8

(42, 42+131, 98)-Net over F₈ — Constructive and digital

Digital (42, 173, 98)-net over F₈, using

t-expansion [i] based on digital (37, 173, 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]

(42, 42+131, 129)-Net over F₈ — Digital

Digital (42, 173, 129)-net over F₈, using

t-expansion [i] based on digital (38, 173, 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]

(42, 42+131, 836)-Net in Base 8 — Upper bound on s

There is no (42, 173, 837)-net in base 8, because

1 times m-reduction [i] would yield (42, 172, 837)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 215204 259947 521220 024303 975201 809123 539410 154210 000465 755494 468193 018091 611646 958486 611672 272380 968687 294184 586557 094191 558259 182937 617845 022027 555688 447092 > 8¹⁷² [i]