MinT - Best Known (37, 37+105, s)-Nets in Base 8

Best Known (37, 37+105, s)-Nets in Base 8

(37, 37+105, 98)-Net over F₈ — Constructive and digital

Digital (37, 142, 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]

(37, 37+105, 121)-Net over F₈ — Digital

Digital (37, 142, 121)-net over F₈, using

net from sequence [i] based on digital (37, 120)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 121, using
  - a curve from the manYPoints database [i]

(37, 37+105, 779)-Net in Base 8 — Upper bound on s

There is no (37, 142, 780)-net in base 8, because

1 times m-reduction [i] would yield (37, 141, 780)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 22 392735 927132 392409 199595 077912 628264 654980 285569 577652 818092 046214 431112 683306 672336 112585 087986 669374 041513 133271 537181 479776 > 8¹⁴¹ [i]