MinT - Best Known (42, 102, s)-Nets in Base 27

Best Known (42, 102, s)-Nets in Base 27

(42, 102, 152)-Net over F₂₇ — Constructive and digital

Digital (42, 102, 152)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (6, 36, 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]
2. digital (6, 66, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇ (see above)

(42, 102, 280)-Net over F₂₇ — Digital

Digital (42, 102, 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]

(42, 102, 370)-Net in Base 27 — Constructive

(42, 102, 370)-net in base 27, using

2 times m-reduction [i] based on (42, 104, 370)-net in base 27, using
- base change [i] based on digital (16, 78, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(42, 102, 34060)-Net in Base 27 — Upper bound on s

There is no (42, 102, 34061)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 99 827002 207900 811096 177855 047075 092172 761635 001245 183162 469349 035826 629078 316483 222575 316970 316038 183013 782630 532652 751458 765488 721666 127391 013921 > 27¹⁰² [i]