MinT - Best Known (147−105, 147, s)-Nets in Base 8

Best Known (147−105, 147, s)-Nets in Base 8

(147−105, 147, 98)-Net over F₈ — Constructive and digital

Digital (42, 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]

(147−105, 147, 129)-Net over F₈ — Digital

Digital (42, 147, 129)-net over F₈, using

t-expansion [i] based on digital (38, 147, 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]

(147−105, 147, 959)-Net in Base 8 — Upper bound on s

There is no (42, 147, 960)-net in base 8, because

1 times m-reduction [i] would yield (42, 146, 960)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 742587 498450 459778 773717 319135 735360 411018 739880 459290 642199 048313 774995 841652 899915 375509 936788 972832 064545 479678 939823 666068 488747 > 8¹⁴⁶ [i]