MinT - Best Known (30, 70, s)-Nets in Base 27

Best Known (30, 70, s)-Nets in Base 27

(30, 70, 140)-Net over F₂₇ — Constructive and digital

Digital (30, 70, 140)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (4, 24, 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, 46, 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]

(30, 70, 172)-Net in Base 27 — Constructive

(30, 70, 172)-net in base 27, using

22 times m-reduction [i] based on (30, 92, 172)-net in base 27, using
- base change [i] based on digital (7, 69, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(30, 70, 215)-Net over F₂₇ — Digital

Digital (30, 70, 215)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(30, 70, 298)-Net in Base 27

(30, 70, 298)-net in base 27, using

2 times m-reduction [i] based on (30, 72, 298)-net in base 27, using
- base change [i] based on digital (12, 54, 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]

(30, 70, 32656)-Net in Base 27 — Upper bound on s

There is no (30, 70, 32657)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 15689 127124 211954 663144 479402 082001 294318 584720 739684 921451 298881 654319 824660 003500 839585 689769 775153 > 27⁷⁰ [i]