MinT - Best Known (99−70, 99, s)-Nets in Base 27

Best Known (99−70, 99, s)-Nets in Base 27

(99−70, 99, 114)-Net over F₂₇ — Constructive and digital

Digital (29, 99, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 99, 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]

(99−70, 99, 150)-Net in Base 27 — Constructive

(29, 99, 150)-net in base 27, using

1 times m-reduction [i] based on (29, 100, 150)-net in base 27, using
- base change [i] based on digital (4, 75, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(99−70, 99, 208)-Net over F₂₇ — Digital

Digital (29, 99, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 99, 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]

(99−70, 99, 5965)-Net in Base 27 — Upper bound on s

There is no (29, 99, 5966)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 5074 433285 867348 950823 474832 620419 920440 394504 989828 064062 662955 378428 926060 298017 108204 500022 943706 735568 252209 897433 597868 325244 680141 232465 > 27⁹⁹ [i]