MinT - Best Known (43, 109, s)-Nets in Base 27

Best Known (43, 109, s)-Nets in Base 27

(43, 109, 140)-Net over F₂₇ — Constructive and digital

Digital (43, 109, 140)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (4, 37, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]
2. digital (6, 72, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(43, 109, 224)-Net in Base 27 — Constructive

(43, 109, 224)-net in base 27, using

27¹ times duplication [i] based on (42, 108, 224)-net in base 27, using
- t-expansion [i] based on (40, 108, 224)-net in base 27, using
  - base change [i] based on digital (13, 81, 224)-net over F₈₁, using
    - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
        a function field by SÃ©mirat [i]

(43, 109, 280)-Net over F₂₇ — Digital

Digital (43, 109, 280)-net over F₂₇, using

t-expansion [i] based on digital (42, 109, 280)-net over F₂₇, using
- net from sequence [i] based on digital (42, 279)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 42 and N(F) ≥ 280, using
    - Drinfeld modules of rank 1 [i]

(43, 109, 298)-Net in Base 27

(43, 109, 298)-net in base 27, using

27¹ times duplication [i] based on (42, 108, 298)-net in base 27, using
- t-expansion [i] based on (39, 108, 298)-net in base 27, using
  - base change [i] based on digital (12, 81, 298)-net over F₈₁, using
    - net from sequence [i] based on digital (12, 297)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 12 and N(F) ≥ 298, using
        a curve from the manYPoints database [i]

(43, 109, 27035)-Net in Base 27 — Upper bound on s

There is no (43, 109, 27036)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1 043963 697413 518992 347909 002206 829157 937458 683364 727112 196507 386208 750500 045731 939798 285773 774239 370384 652320 210303 727386 864081 040775 006712 646349 224119 150041 > 27¹⁰⁹ [i]