MinT - Best Known (150−95, 150, s)-Nets in Base 8

Best Known (150−95, 150, s)-Nets in Base 8

(150−95, 150, 98)-Net over F₈ — Constructive and digital

Digital (55, 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]

(150−95, 150, 144)-Net over F₈ — Digital

Digital (55, 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]

(150−95, 150, 1884)-Net in Base 8 — Upper bound on s

There is no (55, 150, 1885)-net in base 8, because

1 times m-reduction [i] would yield (55, 149, 1885)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 366 726261 771500 195933 250882 528495 262040 994241 178475 777472 483955 493877 972860 511120 130655 777361 985290 506477 705634 512473 236462 514520 195296 > 8¹⁴⁹ [i]