MinT - Best Known (99−71, 99, s)-Nets in Base 27

Best Known (99−71, 99, s)-Nets in Base 27

(99−71, 99, 114)-Net over F₂₇ — Constructive and digital

Digital (28, 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]

(99−71, 99, 116)-Net in Base 27 — Constructive

(28, 99, 116)-net in base 27, using

5 times m-reduction [i] based on (28, 104, 116)-net in base 27, using
- base change [i] based on digital (2, 78, 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]

(99−71, 99, 208)-Net over F₂₇ — Digital

Digital (28, 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]

(99−71, 99, 5428)-Net in Base 27 — Upper bound on s

There is no (28, 99, 5429)-net in base 27, because

1 times m-reduction [i] would yield (28, 98, 5429)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 188 916692 539539 416904 359830 584953 842298 482616 388626 060206 488260 456168 043806 449428 935604 538155 506721 579968 610716 577533 514752 666288 013854 974611 > 27⁹⁸ [i]