MinT - Best Known (38, 38+57, s)-Nets in Base 27

Best Known (38, 38+57, s)-Nets in Base 27

(38, 38+57, 140)-Net over F₂₇ — Constructive and digital

Digital (38, 95, 140)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (4, 32, 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 (6, 63, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(38, 38+57, 224)-Net in Base 27 — Constructive

(38, 95, 224)-net in base 27, using

5 times m-reduction [i] based on (38, 100, 224)-net in base 27, using
- base change [i] based on digital (13, 75, 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]

(38, 38+57, 244)-Net over F₂₇ — Digital

Digital (38, 95, 244)-net over F₂₇, using

t-expansion [i] based on digital (36, 95, 244)-net over F₂₇, using
- net from sequence [i] based on digital (36, 243)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 36 and N(F) ≥ 244, using
    - Drinfeld modules of rank 1 [i]

(38, 38+57, 298)-Net in Base 27

(38, 95, 298)-net in base 27, using

9 times m-reduction [i] based on (38, 104, 298)-net in base 27, using
- base change [i] based on digital (12, 78, 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]

(38, 38+57, 27739)-Net in Base 27 — Upper bound on s

There is no (38, 95, 27740)-net in base 27, because

1 times m-reduction [i] would yield (38, 94, 27740)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 353 574789 103418 438881 252377 846792 616285 966832 728169 604386 227488 555103 132050 526890 128010 861819 329156 367752 087497 517251 844754 770457 923521 > 27⁹⁴ [i]