MinT - Best Known (29, 29+72, s)-Nets in Base 27

Best Known (29, 29+72, s)-Nets in Base 27

(29, 29+72, 114)-Net over F₂₇ — Constructive and digital

Digital (29, 101, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 101, 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]

(29, 29+72, 116)-Net in Base 27 — Constructive

(29, 101, 116)-net in base 27, using

7 times m-reduction [i] based on (29, 108, 116)-net in base 27, using
- base change [i] based on digital (2, 81, 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]

(29, 29+72, 208)-Net over F₂₇ — Digital

Digital (29, 101, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 101, 208)-net over F₂₇, using
- net from sequence [i] based on digital (24, 207)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 24 and N(F) ≥ 208, using
    - an algebraic function field by Beelen and Pellikaan [i]

(29, 29+72, 5676)-Net in Base 27 — Upper bound on s

There is no (29, 101, 5677)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 3 703990 479846 053491 376749 861452 837707 489273 948310 865137 849758 046431 623657 700050 219154 759707 410043 398194 262281 438860 170026 553880 110062 903676 005553 > 27¹⁰¹ [i]