MinT - Best Known (75−52, 75, s)-Nets in Base 27

Best Known (75−52, 75, s)-Nets in Base 27

(75−52, 75, 114)-Net over F₂₇ — Constructive and digital

Digital (23, 75, 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]

(75−52, 75, 150)-Net in Base 27 — Constructive

(23, 75, 150)-net in base 27, using

1 times m-reduction [i] based on (23, 76, 150)-net in base 27, using
- base change [i] based on digital (4, 57, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(75−52, 75, 163)-Net over F₂₇ — Digital

Digital (23, 75, 163)-net over F₂₇, using

t-expansion [i] based on digital (21, 75, 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]

(75−52, 75, 5447)-Net in Base 27 — Upper bound on s

There is no (23, 75, 5448)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 225830 634585 774672 073646 630586 554732 308151 647811 352000 151677 366332 075618 967014 268151 781035 145468 993088 175281 > 27⁷⁵ [i]