MinT - Best Known (27, 27+48, s)-Nets in Base 81

Best Known (27, 27+48, s)-Nets in Base 81

(27, 27+48, 370)-Net over F₈₁ — Constructive and digital

Digital (27, 75, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 75, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(27, 27+48, 500)-Net over F₈₁ — Digital

Digital (27, 75, 500)-net over F₈₁, using

t-expansion [i] based on digital (26, 75, 500)-net over F₈₁, using
- net from sequence [i] based on digital (26, 499)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 26 and N(F) ≥ 500, using
    - a curve from the manYPoints database [i]

(27, 27+48, 112782)-Net in Base 81 — Upper bound on s

There is no (27, 75, 112783)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 136896 353367 582072 006271 020099 409317 619863 335781 485993 204459 740045 556896 033454 940022 572984 915757 770961 655118 154470 693889 663191 519962 560221 253761 > 81⁷⁵ [i]