MinT - Best Known (89−65, 89, s)-Nets in Base 27

Best Known (89−65, 89, s)-Nets in Base 27

(89−65, 89, 114)-Net over F₂₇ — Constructive and digital

Digital (24, 89, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 89, 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]

(89−65, 89, 208)-Net over F₂₇ — Digital

Digital (24, 89, 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]

(89−65, 89, 4231)-Net in Base 27 — Upper bound on s

There is no (24, 89, 4232)-net in base 27, because

1 times m-reduction [i] would yield (24, 88, 4232)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 918802 438399 717026 703380 064682 747984 418371 282465 436761 845748 714495 820744 490770 369310 613855 964798 743409 130375 864282 809183 531009 > 27⁸⁸ [i]