MinT - Best Known (34, 79, s)-Nets in Base 32

Best Known (34, 79, s)-Nets in Base 32

(34, 79, 174)-Net over F₃₂ — Constructive and digital

Digital (34, 79, 174)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (5, 27, 76)-net over F₃₂, using
  - net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]
2. digital (7, 52, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]

(34, 79, 276)-Net over F₃₂ — Digital

Digital (34, 79, 276)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(34, 79, 288)-Net in Base 32 — Constructive

(34, 79, 288)-net in base 32, using

t-expansion [i] based on (33, 79, 288)-net in base 32, using
- 5 times m-reduction [i] based on (33, 84, 288)-net in base 32, using
  - base change [i] based on digital (9, 60, 288)-net over F₁₂₈, using
    - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(34, 79, 342)-Net in Base 32

(34, 79, 342)-net in base 32, using

5 times m-reduction [i] based on (34, 84, 342)-net in base 32, using
- base change [i] based on digital (20, 70, 342)-net over F₆₄, using
  - net from sequence [i] based on digital (20, 341)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
      - a curve from the manYPoints database [i]

(34, 79, 63365)-Net in Base 32 — Upper bound on s

There is no (34, 79, 63366)-net in base 32, because

1 times m-reduction [i] would yield (34, 78, 63366)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2521 849265 646934 040633 445289 030457 057337 165771 903995 568981 613052 068609 973269 601019 483831 067995 787809 962906 457774 378048 > 32⁷⁸ [i]