MinT - Best Known (96−70, 96, s)-Nets in Base 27

Best Known (96−70, 96, s)-Nets in Base 27

(96−70, 96, 114)-Net over F₂₇ — Constructive and digital

Digital (26, 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]

(96−70, 96, 116)-Net in Base 27 — Constructive

(26, 96, 116)-net in base 27, using

base change [i] based on digital (2, 72, 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]

(96−70, 96, 208)-Net over F₂₇ — Digital

Digital (26, 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]

(96−70, 96, 4493)-Net in Base 27 — Upper bound on s

There is no (26, 96, 4494)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 259336 142470 244325 594853 438300 972853 882759 574139 732830 146543 934144 330501 090720 040486 733853 565881 772055 272490 158954 823374 822165 226179 496529 > 27⁹⁶ [i]