MinT - Best Known (13, 48, s)-Nets in Base 27

Best Known (13, 48, s)-Nets in Base 27

(13, 48, 96)-Net over F₂₇ — Constructive and digital

Digital (13, 48, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 48, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(13, 48, 100)-Net in Base 27 — Constructive

(13, 48, 100)-net in base 27, using

base change [i] based on digital (1, 36, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(13, 48, 136)-Net over F₂₇ — Digital

Digital (13, 48, 136)-net over F₂₇, using

net from sequence [i] based on digital (13, 135)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 13 and N(F) ≥ 136, using
  - a curve from the manYPoints database [i]

(13, 48, 2493)-Net in Base 27 — Upper bound on s

There is no (13, 48, 2494)-net in base 27, because

1 times m-reduction [i] would yield (13, 47, 2494)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 18 891706 995662 426029 076030 445958 635938 599470 316424 073693 844178 702637 > 27⁴⁷ [i]