MinT - Best Known (88−63, 88, s)-Nets in Base 27

Best Known (88−63, 88, s)-Nets in Base 27

(88−63, 88, 114)-Net over F₂₇ — Constructive and digital

Digital (25, 88, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 88, 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]

(88−63, 88, 116)-Net in Base 27 — Constructive

(25, 88, 116)-net in base 27, using

4 times m-reduction [i] based on (25, 92, 116)-net in base 27, using
- base change [i] based on digital (2, 69, 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]

(88−63, 88, 208)-Net over F₂₇ — Digital

Digital (25, 88, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 88, 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]

(88−63, 88, 4951)-Net in Base 27 — Upper bound on s

There is no (25, 88, 4952)-net in base 27, because

1 times m-reduction [i] would yield (25, 87, 4952)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 33983 682029 593234 529457 352080 126071 615218 540995 909308 777808 164279 043506 918809 941538 053904 306373 760638 376559 434939 402173 270625 > 27⁸⁷ [i]