MinT - Best Known (15, 53, s)-Nets in Base 81

Best Known (15, 53, s)-Nets in Base 81

(15, 53, 224)-Net over F₈₁ — Constructive and digital

Digital (15, 53, 224)-net over F₈₁, using

t-expansion [i] based on digital (13, 53, 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, 53, 298)-Net over F₈₁ — Digital

Digital (15, 53, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 53, 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, 53, 20873)-Net in Base 81 — Upper bound on s

There is no (15, 53, 20874)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 141180 115200 423417 589599 348270 978609 211278 432222 500509 204235 668185 052543 737330 855226 132554 528646 928481 > 81⁵³ [i]