MinT - Best Known (94−69, 94, s)-Nets in Base 27

Best Known (94−69, 94, s)-Nets in Base 27

(94−69, 94, 114)-Net over F₂₇ — Constructive and digital

Digital (25, 94, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 94, 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]

(94−69, 94, 208)-Net over F₂₇ — Digital

Digital (25, 94, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 94, 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]

(94−69, 94, 4264)-Net in Base 27 — Upper bound on s

There is no (25, 94, 4265)-net in base 27, because

1 times m-reduction [i] would yield (25, 93, 4265)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 13 111247 410977 666829 263044 714889 453329 876023 725693 057197 681029 438289 107189 698903 684943 459948 333633 201870 331504 064045 682312 655090 572393 > 27⁹³ [i]