MinT - Best Known (102−40, 102, s)-Nets in Base 27

Best Known (102−40, 102, s)-Nets in Base 27

(102−40, 102, 276)-Net over F₂₇ — Constructive and digital

Digital (62, 102, 276)-net over F₂₇, using

1 times m-reduction [i] based on digital (62, 103, 276)-net over F₂₇, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (9, 22, 88)-net over F₂₇, using
    - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
        a function field by SÃ©mirat [i]
  2. digital (10, 30, 94)-net over F₂₇, using
    - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
        a function field by SÃ©mirat [i]
  3. digital (10, 51, 94)-net over F₂₇, using
    - net from sequence [i] based on digital (10, 93)-sequence over F₂₇ (see above)

(102−40, 102, 730)-Net in Base 27 — Constructive

(62, 102, 730)-net in base 27, using

2 times m-reduction [i] based on (62, 104, 730)-net in base 27, using
- base change [i] based on digital (36, 78, 730)-net over F₈₁, using
  - net from sequence [i] based on digital (36, 729)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 36 and N(F) ≥ 730, using
      - the Hermitian function field over F₈₁ [i]

(102−40, 102, 3301)-Net over F₂₇ — Digital

Digital (62, 102, 3301)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−40, 102, 6372170)-Net in Base 27 — Upper bound on s

There is no (62, 102, 6372171)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 99 794079 329027 246424 662087 352973 008228 152314 794789 353334 716691 343429 905925 414497 475011 132638 894057 538293 579284 800256 468979 098935 954464 127522 009561 > 27¹⁰² [i]