MinT - Best Known (96−65, 96, s)-Nets in Base 27

Best Known (96−65, 96, s)-Nets in Base 27

(96−65, 96, 114)-Net over F₂₇ — Constructive and digital

Digital (31, 96, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 96, 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]

(96−65, 96, 172)-Net in Base 27 — Constructive

(31, 96, 172)-net in base 27, using

base change [i] based on digital (7, 72, 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]

(96−65, 96, 208)-Net over F₂₇ — Digital

Digital (31, 96, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 96, 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]

(96−65, 96, 8718)-Net in Base 27 — Upper bound on s

There is no (31, 96, 8719)-net in base 27, because

1 times m-reduction [i] would yield (31, 95, 8719)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 9561 801614 541792 045171 794262 751900 412232 823246 061941 066132 560703 514161 412253 705546 827290 105912 414120 309477 257719 895958 539612 599243 466945 > 27⁹⁵ [i]