MinT - Best Known (46, 46+29, s)-Nets in Base 27

Best Known (46, 46+29, s)-Nets in Base 27

(46, 46+29, 256)-Net over F₂₇ — Constructive and digital

Digital (46, 75, 256)-net over F₂₇, using

generalized (u,Â u+v)-construction [i] based on
1. digital (4, 11, 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 (4, 13, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇ (see above)
3. digital (4, 18, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇ (see above)
4. digital (4, 33, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇ (see above)

(46, 46+29, 408)-Net in Base 27 — Constructive

(46, 75, 408)-net in base 27, using

(u,Â u+v)-construction [i] based on
1. digital (1, 15, 38)-net over F₂₇, using
  - net from sequence [i] based on digital (1, 37)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]
2. (31, 60, 370)-net in base 27, using
  - base change [i] based on digital (16, 45, 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]

(46, 46+29, 2979)-Net over F₂₇ — Digital

Digital (46, 75, 2979)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 46+29, large)-Net in Base 27 — Upper bound on s

There is no (46, 75, large)-net in base 27, because

27 times m-reduction [i] would yield (46, 48, large)-net in base 27, but
- mutually orthogonal hypercube bound [i]