MinT - Best Known (30, 30+67, s)-Nets in Base 27

Best Known (30, 30+67, s)-Nets in Base 27

(30, 30+67, 114)-Net over F₂₇ — Constructive and digital

Digital (30, 97, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 97, 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+67, 160)-Net in Base 27 — Constructive

(30, 97, 160)-net in base 27, using

3 times m-reduction [i] based on (30, 100, 160)-net in base 27, using
- base change [i] based on digital (5, 75, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(30, 30+67, 208)-Net over F₂₇ — Digital

Digital (30, 97, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 97, 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+67, 7367)-Net in Base 27 — Upper bound on s

There is no (30, 97, 7368)-net in base 27, because

1 times m-reduction [i] would yield (30, 96, 7368)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 257932 645930 274708 220411 507712 708217 519815 109446 200665 645864 417944 813840 702684 760822 904969 504891 772349 693297 735345 786778 113881 703516 849745 > 27⁹⁶ [i]