MinT - Best Known (23, 23+43, s)-Nets in Base 27

Best Known (23, 23+43, s)-Nets in Base 27

(23, 23+43, 114)-Net over F₂₇ — Constructive and digital

Digital (23, 66, 114)-net over F₂₇, using

net from sequence [i] based on digital (23, 113)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 23 and N(F) ≥ 114, using
  - an explicitly constructive algebraic function field [i]

(23, 23+43, 160)-Net in Base 27 — Constructive

(23, 66, 160)-net in base 27, using

6 times m-reduction [i] based on (23, 72, 160)-net in base 27, using
- base change [i] based on digital (5, 54, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(23, 23+43, 163)-Net over F₂₇ — Digital

Digital (23, 66, 163)-net over F₂₇, using

t-expansion [i] based on digital (21, 66, 163)-net over F₂₇, using
- net from sequence [i] based on digital (21, 162)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 21 and N(F) ≥ 163, using
    - a curve from the manYPoints database [i]

(23, 23+43, 190)-Net in Base 27

(23, 66, 190)-net in base 27, using

2 times m-reduction [i] based on (23, 68, 190)-net in base 27, using
- base change [i] based on digital (6, 51, 190)-net over F₈₁, using
  - net from sequence [i] based on digital (6, 189)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 6 and N(F) ≥ 190, using
      - a curve from the manYPoints database [i]

(23, 23+43, 8982)-Net in Base 27 — Upper bound on s

There is no (23, 66, 8983)-net in base 27, because

1 times m-reduction [i] would yield (23, 65, 8983)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1093 726975 873692 384721 626705 711340 536023 747993 915325 476294 145364 129295 018313 717509 754725 325327 > 27⁶⁵ [i]