MinT - Best Known (30, 91, s)-Nets in Base 27

Best Known (30, 91, s)-Nets in Base 27

(30, 91, 114)-Net over F₂₇ — Constructive and digital

Digital (30, 91, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 91, 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, 91, 172)-Net in Base 27 — Constructive

(30, 91, 172)-net in base 27, using

1 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, 91, 208)-Net over F₂₇ — Digital

Digital (30, 91, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 91, 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, 91, 9102)-Net in Base 27 — Upper bound on s

There is no (30, 91, 9103)-net in base 27, because

1 times m-reduction [i] would yield (30, 90, 9103)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 665 968469 090227 531936 185055 867598 098928 895679 814604 499701 386917 179959 824932 226415 401441 580547 524192 287226 001224 904523 447345 257877 > 27⁹⁰ [i]