MinT - Best Known (48, 106, s)-Nets in Base 27

Best Known (48, 106, s)-Nets in Base 27

(48, 106, 182)-Net over F₂₇ — Constructive and digital

Digital (48, 106, 182)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (9, 38, 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, 68, 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]

(48, 106, 370)-Net in Base 27 — Constructive

(48, 106, 370)-net in base 27, using

t-expansion [i] based on (43, 106, 370)-net in base 27, using
- 2 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]

(48, 106, 381)-Net over F₂₇ — Digital

Digital (48, 106, 381)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 106, 76549)-Net in Base 27 — Upper bound on s

There is no (48, 106, 76550)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 53 037794 947888 584576 791340 586355 292799 984246 154309 506941 240703 787856 830913 220038 832468 843834 894293 057244 339913 777676 672845 598394 907327 361732 266289 596613 > 27¹⁰⁶ [i]