MinT - Best Known (83−49, 83, s)-Nets in Base 32

Best Known (83−49, 83, s)-Nets in Base 32

(83−49, 83, 162)-Net over F₃₂ — Constructive and digital

Digital (34, 83, 162)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (3, 27, 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 (7, 56, 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]

(83−49, 83, 273)-Net over F₃₂ — Digital

Digital (34, 83, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 83, 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]

(83−49, 83, 288)-Net in Base 32 — Constructive

(34, 83, 288)-net in base 32, using

t-expansion [i] based on (33, 83, 288)-net in base 32, using
- 1 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]

(83−49, 83, 342)-Net in Base 32

(34, 83, 342)-net in base 32, using

1 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]

(83−49, 83, 43901)-Net in Base 32 — Upper bound on s

There is no (34, 83, 43902)-net in base 32, because

1 times m-reduction [i] would yield (34, 82, 43902)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2645 524719 211430 578931 029033 332064 022726 647676 827249 676214 023351 490894 822165 200566 501335 308301 251329 935897 824044 477833 519373 > 32⁸² [i]