MinT - Best Known (48, 48+60, s)-Nets in Base 27

Best Known (48, 48+60, s)-Nets in Base 27

(48, 48+60, 178)-Net over F₂₇ — Constructive and digital

Digital (48, 108, 178)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (8, 38, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]
2. digital (10, 70, 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, 48+60, 355)-Net over F₂₇ — Digital

Digital (48, 108, 355)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 48+60, 370)-Net in Base 27 — Constructive

(48, 108, 370)-net in base 27, using

t-expansion [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, 48+60, 65859)-Net in Base 27 — Upper bound on s

There is no (48, 108, 65860)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 38662 360322 384669 335156 634603 926813 098136 955263 291197 602698 918476 801704 831490 299918 669632 621737 260200 548500 001560 002373 141098 594070 167885 240307 642533 268313 > 27¹⁰⁸ [i]