MinT - Best Known (112−75, 112, s)-Nets in Base 8

Best Known (112−75, 112, s)-Nets in Base 8

(112−75, 112, 98)-Net over F₈ — Constructive and digital

Digital (37, 112, 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]

(112−75, 112, 121)-Net over F₈ — Digital

Digital (37, 112, 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]

(112−75, 112, 1048)-Net in Base 8 — Upper bound on s

There is no (37, 112, 1049)-net in base 8, because

1 times m-reduction [i] would yield (37, 111, 1049)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 17745 326882 919353 596091 427482 895077 793245 720691 470320 384700 211118 979277 824159 830381 082850 782969 130240 > 8¹¹¹ [i]