MinT - Best Known (35, 94, s)-Nets in Base 32

Best Known (35, 94, s)-Nets in Base 32

(35, 94, 128)-Net over F₃₂ — Constructive and digital

Digital (35, 94, 128)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (3, 32, 64)-net over F₃₂, using
  - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]
2. digital (3, 62, 64)-net over F₃₂, using
  - net from sequence [i] based on digital (3, 63)-sequence over F₃₂ (see above)

(35, 94, 216)-Net in Base 32 — Constructive

(35, 94, 216)-net in base 32, using

11 times m-reduction [i] based on (35, 105, 216)-net in base 32, using
- base change [i] based on digital (5, 75, 216)-net over F₁₂₈, using
  - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
      - a function field by SÃ©mirat [i]

(35, 94, 273)-Net over F₃₂ — Digital

Digital (35, 94, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 94, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(35, 94, 315)-Net in Base 32

(35, 94, 315)-net in base 32, using

2 times m-reduction [i] based on (35, 96, 315)-net in base 32, using
- base change [i] based on digital (19, 80, 315)-net over F₆₄, using
  - net from sequence [i] based on digital (19, 314)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 19 and N(F) ≥ 315, using
      - a curve from the manYPoints database [i]

(35, 94, 25255)-Net in Base 32 — Upper bound on s

There is no (35, 94, 25256)-net in base 32, because

1 times m-reduction [i] would yield (35, 93, 25256)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 95 272507 438509 316729 929595 711574 484707 065962 613885 827565 408995 497516 052347 990355 336753 911864 198858 021133 433218 694366 453388 346357 018058 488092 > 32⁹³ [i]