MinT - Best Known (99−72, 99, s)-Nets in Base 27

Best Known (99−72, 99, s)-Nets in Base 27

(99−72, 99, 114)-Net over F₂₇ — Constructive and digital

Digital (27, 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]

(99−72, 99, 116)-Net in Base 27 — Constructive

(27, 99, 116)-net in base 27, using

1 times m-reduction [i] based on (27, 100, 116)-net in base 27, using
- base change [i] based on digital (2, 75, 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]

(99−72, 99, 208)-Net over F₂₇ — Digital

Digital (27, 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]

(99−72, 99, 4723)-Net in Base 27 — Upper bound on s

There is no (27, 99, 4724)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 5081 390432 630966 573400 372322 293552 950274 027362 883918 336344 544218 364315 178955 850382 161488 911763 743365 395621 659891 570665 184817 511286 200335 657025 > 27⁹⁹ [i]