MinT - Best Known (24, 24+49, s)-Nets in Base 27

Best Known (24, 24+49, s)-Nets in Base 27

(24, 24+49, 114)-Net over F₂₇ — Constructive and digital

Digital (24, 73, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 73, 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+49, 160)-Net in Base 27 — Constructive

(24, 73, 160)-net in base 27, using

3 times m-reduction [i] based on (24, 76, 160)-net in base 27, using
- base change [i] based on digital (5, 57, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(24, 24+49, 208)-Net over F₂₇ — Digital

Digital (24, 73, 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+49, 7408)-Net in Base 27 — Upper bound on s

There is no (24, 73, 7409)-net in base 27, because

1 times m-reduction [i] would yield (24, 72, 7409)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 11 437750 837054 244612 019575 524645 854520 486485 537809 575297 812173 999779 299949 985467 124349 373357 003417 899681 > 27⁷² [i]