MinT - Best Known (109−74, 109, s)-Nets in Base 27

Best Known (109−74, 109, s)-Nets in Base 27

(109−74, 109, 114)-Net over F₂₇ — Constructive and digital

Digital (35, 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]

(109−74, 109, 172)-Net in Base 27 — Constructive

(35, 109, 172)-net in base 27, using

27¹ times duplication [i] based on (34, 108, 172)-net in base 27, using
- base change [i] based on digital (7, 81, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(109−74, 109, 220)-Net over F₂₇ — Digital

Digital (35, 109, 220)-net over F₂₇, using

t-expansion [i] based on digital (33, 109, 220)-net over F₂₇, using
- net from sequence [i] based on digital (33, 219)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 33 and N(F) ≥ 220, using
    - Drinfeld modules of rank 1 [i]

(109−74, 109, 9262)-Net in Base 27 — Upper bound on s

There is no (35, 109, 9263)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1 044075 002580 691847 596619 063801 968131 889698 801239 030489 509697 904450 904363 620912 158717 395016 675372 495791 087076 006098 401078 867746 116246 034959 121872 066773 644703 > 27¹⁰⁹ [i]