MinT - Best Known (147−101, 147, s)-Nets in Base 8

Best Known (147−101, 147, s)-Nets in Base 8

(147−101, 147, 98)-Net over F₈ — Constructive and digital

Digital (46, 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]

(147−101, 147, 144)-Net over F₈ — Digital

Digital (46, 147, 144)-net over F₈, using

t-expansion [i] based on digital (45, 147, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(147−101, 147, 1175)-Net in Base 8 — Upper bound on s

There is no (46, 147, 1176)-net in base 8, because

1 times m-reduction [i] would yield (46, 146, 1176)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 731598 699687 668047 072561 036449 602889 654062 868061 853417 244823 315402 554110 915403 907713 625405 072049 143800 683786 701835 214419 729590 827012 > 8¹⁴⁶ [i]