MinT - Best Known (30, 30+56, s)-Nets in Base 27

Best Known (30, 30+56, s)-Nets in Base 27

(30, 30+56, 114)-Net over F₂₇ — Constructive and digital

Digital (30, 86, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 86, 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]

(30, 30+56, 172)-Net in Base 27 — Constructive

(30, 86, 172)-net in base 27, using

6 times m-reduction [i] based on (30, 92, 172)-net in base 27, using
- base change [i] based on digital (7, 69, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(30, 30+56, 208)-Net over F₂₇ — Digital

Digital (30, 86, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 86, 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]

(30, 30+56, 226)-Net in Base 27

(30, 86, 226)-net in base 27, using

2 times m-reduction [i] based on (30, 88, 226)-net in base 27, using
- base change [i] based on digital (8, 66, 226)-net over F₈₁, using
  - net from sequence [i] based on digital (8, 225)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 8 and N(F) ≥ 226, using
      - a curve from the manYPoints database [i]

(30, 30+56, 10808)-Net in Base 27 — Upper bound on s

There is no (30, 86, 10809)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1251 672161 390555 482888 223079 424473 202317 379534 906943 327362 215808 881888 662723 644661 482808 045274 631033 716194 395760 180127 491537 > 27⁸⁶ [i]