MinT - Best Known (41, 102, s)-Nets in Base 27

Best Known (41, 102, s)-Nets in Base 27

(41, 102, 146)-Net over F₂₇ — Constructive and digital

Digital (41, 102, 146)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (4, 34, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]
2. digital (7, 68, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(41, 102, 224)-Net in Base 27 — Constructive

(41, 102, 224)-net in base 27, using

t-expansion [i] based on (40, 102, 224)-net in base 27, using
- 6 times m-reduction [i] based on (40, 108, 224)-net in base 27, using
  - base change [i] based on digital (13, 81, 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]

(41, 102, 273)-Net over F₂₇ — Digital

Digital (41, 102, 273)-net over F₂₇, using

t-expansion [i] based on digital (40, 102, 273)-net over F₂₇, using
- net from sequence [i] based on digital (40, 272)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 40 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(41, 102, 298)-Net in Base 27

(41, 102, 298)-net in base 27, using

t-expansion [i] based on (39, 102, 298)-net in base 27, using
- 6 times m-reduction [i] based on (39, 108, 298)-net in base 27, using
  - base change [i] based on digital (12, 81, 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]

(41, 102, 30515)-Net in Base 27 — Upper bound on s

There is no (41, 102, 30516)-net in base 27, because

1 times m-reduction [i] would yield (41, 101, 30516)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 3 698703 302649 492937 077574 891012 282254 743146 787026 227197 555073 590069 873178 131037 520262 175581 777811 983995 099901 082740 364804 905644 628264 708579 162105 > 27¹⁰¹ [i]