MinT - Best Known (115−72, 115, s)-Nets in Base 8

Best Known (115−72, 115, s)-Nets in Base 8

(115−72, 115, 98)-Net over F₈ — Constructive and digital

Digital (43, 115, 98)-net over F₈, using

t-expansion [i] based on digital (37, 115, 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]

(115−72, 115, 129)-Net over F₈ — Digital

Digital (43, 115, 129)-net over F₈, using

t-expansion [i] based on digital (38, 115, 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]

(115−72, 115, 1542)-Net in Base 8 — Upper bound on s

There is no (43, 115, 1543)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 72 600105 640992 413579 439574 327873 761175 428360 964550 182125 839831 154200 726319 879000 268019 506081 157550 220720 > 8¹¹⁵ [i]