MinT - Best Known (109−82, 109, s)-Nets in Base 27

Best Known (109−82, 109, s)-Nets in Base 27

(109−82, 109, 114)-Net over F₂₇ — Constructive and digital

Digital (27, 109, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 109, 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]

(109−82, 109, 208)-Net over F₂₇ — Digital

Digital (27, 109, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 109, 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]

(109−82, 109, 3943)-Net in Base 27 — Upper bound on s

There is no (27, 109, 3944)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1 046944 477029 735296 328828 189981 531687 806541 048474 591332 821136 292842 893626 665311 435442 997545 341366 627850 351119 180763 142680 636340 757395 645228 122426 762668 054545 > 27¹⁰⁹ [i]