MinT - Best Known (103−60, 103, s)-Nets in Base 27

Best Known (103−60, 103, s)-Nets in Base 27

(103−60, 103, 158)-Net over F₂₇ — Constructive and digital

Digital (43, 103, 158)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (6, 36, 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]
2. digital (7, 67, 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]

(103−60, 103, 280)-Net over F₂₇ — Digital

Digital (43, 103, 280)-net over F₂₇, using

t-expansion [i] based on digital (42, 103, 280)-net over F₂₇, using
- net from sequence [i] based on digital (42, 279)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 42 and N(F) ≥ 280, using
    - Drinfeld modules of rank 1 [i]

(103−60, 103, 370)-Net in Base 27 — Constructive

(43, 103, 370)-net in base 27, using

5 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 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]

(103−60, 103, 38017)-Net in Base 27 — Upper bound on s

There is no (43, 103, 38018)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 2695 140168 773194 294590 854448 117499 519906 378543 772557 516800 379387 641271 380861 434095 678404 126561 057715 413375 669684 998064 874367 672845 143389 233181 905005 > 27¹⁰³ [i]