MinT - Best Known (83−60, 83, s)-Nets in Base 27

Best Known (83−60, 83, s)-Nets in Base 27

(83−60, 83, 114)-Net over F₂₇ — Constructive and digital

Digital (23, 83, 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]

(83−60, 83, 116)-Net in Base 27 — Constructive

(23, 83, 116)-net in base 27, using

1 times m-reduction [i] based on (23, 84, 116)-net in base 27, using
- base change [i] based on digital (2, 63, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(83−60, 83, 163)-Net over F₂₇ — Digital

Digital (23, 83, 163)-net over F₂₇, using

t-expansion [i] based on digital (21, 83, 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]

(83−60, 83, 4210)-Net in Base 27 — Upper bound on s

There is no (23, 83, 4211)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 63885 286852 347679 499936 955473 309630 131103 752404 601324 794087 122894 593984 740889 648779 109996 563069 630633 363078 313277 457085 > 27⁸³ [i]