MinT - Best Known (48, 110, s)-Nets in Base 27

Best Known (48, 110, s)-Nets in Base 27

(48, 110, 176)-Net over F₂₇ — Constructive and digital

Digital (48, 110, 176)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (7, 38, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]
2. digital (10, 72, 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, 110, 333)-Net over F₂₇ — Digital

Digital (48, 110, 333)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 110, 370)-Net in Base 27 — Constructive

(48, 110, 370)-net in base 27, using

27² times duplication [i] based on (46, 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, 110, 57275)-Net in Base 27 — Upper bound on s

There is no (48, 110, 57276)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 28 190997 917285 843101 615693 658427 628178 371352 251858 279374 680419 085281 291031 431027 586024 629807 486825 359763 463836 399407 095224 855045 022716 810632 411942 854062 705137 > 27¹¹⁰ [i]