MinT - Best Known (24, 24+60, s)-Nets in Base 27

Best Known (24, 24+60, s)-Nets in Base 27

(24, 24+60, 114)-Net over F₂₇ — Constructive and digital

Digital (24, 84, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 84, 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]

(24, 24+60, 116)-Net in Base 27 — Constructive

(24, 84, 116)-net in base 27, using

4 times m-reduction [i] based on (24, 88, 116)-net in base 27, using
- base change [i] based on digital (2, 66, 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]

(24, 24+60, 208)-Net over F₂₇ — Digital

Digital (24, 84, 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]

(24, 24+60, 4701)-Net in Base 27 — Upper bound on s

There is no (24, 84, 4702)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1 726992 448336 668183 455706 626667 318540 437477 316929 903108 570951 743406 943465 388846 417728 421288 585526 661436 862358 906397 435605 > 27⁸⁴ [i]