MinT - Best Known (108−81, 108, s)-Nets in Base 27

Best Known (108−81, 108, s)-Nets in Base 27

(108−81, 108, 114)-Net over F₂₇ — Constructive and digital

Digital (27, 108, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 108, 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]

(108−81, 108, 208)-Net over F₂₇ — Digital

Digital (27, 108, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 108, 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]

(108−81, 108, 4068)-Net in Base 27 — Upper bound on s

There is no (27, 108, 4069)-net in base 27, because

1 times m-reduction [i] would yield (27, 107, 4069)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1433 121785 875815 848086 819917 546804 775560 610388 885071 552909 184162 493530 042154 070042 874755 053043 004352 215999 141651 425002 662995 916354 388405 829135 609919 172897 > 27¹⁰⁷ [i]