MinT - Best Known (47, 47+103, s)-Nets in Base 8

Best Known (47, 47+103, s)-Nets in Base 8

(47, 47+103, 98)-Net over F₈ — Constructive and digital

Digital (47, 150, 98)-net over F₈, using

t-expansion [i] based on digital (37, 150, 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]

(47, 47+103, 144)-Net over F₈ — Digital

Digital (47, 150, 144)-net over F₈, using

t-expansion [i] based on digital (45, 150, 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]

(47, 47+103, 1201)-Net in Base 8 — Upper bound on s

There is no (47, 150, 1202)-net in base 8, because

1 times m-reduction [i] would yield (47, 149, 1202)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 368 980414 116177 532519 678756 617717 838944 732140 538240 901002 407467 262054 672159 541835 615943 263833 063922 000076 596626 355113 711906 739654 266880 > 8¹⁴⁹ [i]