MinT - Best Known (103−72, 103, s)-Nets in Base 27

Best Known (103−72, 103, s)-Nets in Base 27

(103−72, 103, 114)-Net over F₂₇ — Constructive and digital

Digital (31, 103, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 103, 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]

(103−72, 103, 160)-Net in Base 27 — Constructive

(31, 103, 160)-net in base 27, using

1 times m-reduction [i] based on (31, 104, 160)-net in base 27, using
- base change [i] based on digital (5, 78, 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]

(103−72, 103, 208)-Net over F₂₇ — Digital

Digital (31, 103, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 103, 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]

(103−72, 103, 6821)-Net in Base 27 — Upper bound on s

There is no (31, 103, 6822)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 2707 201046 679941 451803 557007 503957 223128 701446 455717 277893 451490 235193 430162 904935 600339 303676 209753 513045 983932 202329 297308 468562 394514 782741 598537 > 27¹⁰³ [i]