MinT - Best Known (28, 28+75, s)-Nets in Base 27

Best Known (28, 28+75, s)-Nets in Base 27

(28, 28+75, 114)-Net over F₂₇ — Constructive and digital

Digital (28, 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]

(28, 28+75, 116)-Net in Base 27 — Constructive

(28, 103, 116)-net in base 27, using

1 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+75, 208)-Net over F₂₇ — Digital

Digital (28, 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]

(28, 28+75, 4956)-Net in Base 27 — Upper bound on s

There is no (28, 103, 4957)-net in base 27, because

1 times m-reduction [i] would yield (28, 102, 4957)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 100 268086 647579 570468 236706 664784 679091 296895 946465 088461 156404 542561 546637 694703 586784 529933 188608 251481 817975 270517 785084 963578 270993 676016 857955 > 27¹⁰² [i]