MinT - Best Known (157−119, 157, s)-Nets in Base 8

Best Known (157−119, 157, s)-Nets in Base 8

(157−119, 157, 98)-Net over F₈ — Constructive and digital

Digital (38, 157, 98)-net over F₈, using

t-expansion [i] based on digital (37, 157, 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]

(157−119, 157, 129)-Net over F₈ — Digital

Digital (38, 157, 129)-net over F₈, using

net from sequence [i] based on digital (38, 128)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
  - a curve from the manYPoints database [i]

(157−119, 157, 759)-Net in Base 8 — Upper bound on s

There is no (38, 157, 760)-net in base 8, because

1 times m-reduction [i] would yield (38, 156, 760)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 797 612572 788540 841084 794478 726025 571936 164379 859443 210344 569724 788372 447760 122709 020830 387451 246773 795656 368137 615295 211215 074929 803010 050680 > 8¹⁵⁶ [i]