MinT - Best Known (118−80, 118, s)-Nets in Base 8

Best Known (118−80, 118, s)-Nets in Base 8

(118−80, 118, 98)-Net over F₈ — Constructive and digital

Digital (38, 118, 98)-net over F₈, using

t-expansion [i] based on digital (37, 118, 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]

(118−80, 118, 129)-Net over F₈ — Digital

Digital (38, 118, 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]

(118−80, 118, 1014)-Net in Base 8 — Upper bound on s

There is no (38, 118, 1015)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 37506 407486 481950 984297 525852 917949 468841 750769 281026 787826 152489 914560 470974 959426 648315 542641 815671 669138 > 8¹¹⁸ [i]