MinT - Best Known (15, 67, s)-Nets in Base 81

Best Known (15, 67, s)-Nets in Base 81

(15, 67, 224)-Net over F₈₁ — Constructive and digital

Digital (15, 67, 224)-net over F₈₁, using

t-expansion [i] based on digital (13, 67, 224)-net over F₈₁, using
- net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
    - a function field by SÃ©mirat [i]

(15, 67, 298)-Net over F₈₁ — Digital

Digital (15, 67, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 67, 298)-net over F₈₁, using
- net from sequence [i] based on digital (12, 297)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 12 and N(F) ≥ 298, using
    - a curve from the manYPoints database [i]

(15, 67, 10907)-Net in Base 81 — Upper bound on s

There is no (15, 67, 10908)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 74 021729 292303 515418 260266 152769 068716 515873 813884 032935 356509 690393 418366 749751 610047 899126 615525 360357 326818 967148 423881 568641 > 81⁶⁷ [i]