MinT - Best Known (14, 35, s)-Nets in Base 81

Best Known (14, 35, s)-Nets in Base 81

(14, 35, 232)-Net over F₈₁ — Constructive and digital

Digital (14, 35, 232)-net over F₈₁, using

(u,Â u+v)-construction [i] based on
1. digital (2, 12, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]
2. digital (2, 23, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁ (see above)

(14, 35, 298)-Net over F₈₁ — Digital

Digital (14, 35, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 35, 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]

(14, 35, 174471)-Net in Base 81 — Upper bound on s

There is no (14, 35, 174472)-net in base 81, because

1 times m-reduction [i] would yield (14, 34, 174472)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 77358 734193 708838 839820 255153 623958 007813 737488 619556 555203 001601 > 81³⁴ [i]