MinT - Best Known (28, 64, s)-Nets in Base 27

Best Known (28, 64, s)-Nets in Base 27

(28, 64, 140)-Net over F₂₇ — Constructive and digital

Digital (28, 64, 140)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (4, 22, 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, 42, 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]

(28, 64, 172)-Net in Base 27 — Constructive

(28, 64, 172)-net in base 27, using

20 times m-reduction [i] based on (28, 84, 172)-net in base 27, using
- base change [i] based on digital (7, 63, 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]

(28, 64, 221)-Net over F₂₇ — Digital

Digital (28, 64, 221)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(28, 64, 298)-Net in Base 27

(28, 64, 298)-net in base 27, using

base change [i] based on digital (12, 48, 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]

(28, 64, 35672)-Net in Base 27 — Upper bound on s

There is no (28, 64, 35673)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 40 486166 245665 764146 282242 147282 967835 285455 832735 594611 126313 275874 662451 910185 122375 499913 > 27⁶⁴ [i]