MinT - Best Known (34, 79, s)-Nets in Base 27

Best Known (34, 79, s)-Nets in Base 27

(34, 79, 152)-Net over F₂₇ — Constructive and digital

Digital (34, 79, 152)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (6, 28, 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, 51, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇ (see above)

(34, 79, 224)-Net in Base 27 — Constructive

(34, 79, 224)-net in base 27, using

5 times m-reduction [i] based on (34, 84, 224)-net in base 27, using
- base change [i] based on digital (13, 63, 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]

(34, 79, 240)-Net over F₂₇ — Digital

Digital (34, 79, 240)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(34, 79, 298)-Net in Base 27

(34, 79, 298)-net in base 27, using

9 times m-reduction [i] based on (34, 88, 298)-net in base 27, using
- base change [i] based on digital (12, 66, 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]

(34, 79, 41361)-Net in Base 27 — Upper bound on s

There is no (34, 79, 41362)-net in base 27, because

1 times m-reduction [i] would yield (34, 78, 41362)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 4430 993653 768871 266584 386021 061436 774795 001642 680965 047293 512936 487879 039520 754409 727083 753105 349014 204589 301117 > 27⁷⁸ [i]