MinT - Best Known (39, 80, s)-Nets in Base 27

Best Known (39, 80, s)-Nets in Base 27

(39, 80, 182)-Net over F₂₇ — Constructive and digital

Digital (39, 80, 182)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (9, 29, 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, 51, 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]

(39, 80, 370)-Net in Base 27 — Constructive

(39, 80, 370)-net in base 27, using

12 times m-reduction [i] based on (39, 92, 370)-net in base 27, using
- base change [i] based on digital (16, 69, 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]

(39, 80, 453)-Net over F₂₇ — Digital

Digital (39, 80, 453)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 80, 143942)-Net in Base 27 — Upper bound on s

There is no (39, 80, 143943)-net in base 27, because

1 times m-reduction [i] would yield (39, 79, 143943)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 119611 511532 928398 132675 865806 251587 269253 134194 199684 617377 051661 096508 414247 022273 835356 185118 664476 229695 449977 > 27⁷⁹ [i]