MinT - Best Known (28, 28+72, s)-Nets in Base 27

Best Known (28, 28+72, s)-Nets in Base 27

(28, 28+72, 114)-Net over F₂₇ — Constructive and digital

Digital (28, 100, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 100, 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]

(28, 28+72, 116)-Net in Base 27 — Constructive

(28, 100, 116)-net in base 27, using

4 times m-reduction [i] based on (28, 104, 116)-net in base 27, using
- base change [i] based on digital (2, 78, 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]

(28, 28+72, 208)-Net over F₂₇ — Digital

Digital (28, 100, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 100, 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]

(28, 28+72, 5178)-Net in Base 27 — Upper bound on s

There is no (28, 100, 5179)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 137473 336575 683906 684910 998138 726898 547034 082944 775677 696003 915649 384970 065906 707675 769927 619326 389192 124659 292582 442236 965917 888229 807149 700665 > 27¹⁰⁰ [i]