MinT - Best Known (97−53, 97, s)-Nets in Base 32

Best Known (97−53, 97, s)-Nets in Base 32

(97−53, 97, 218)-Net over F₃₂ — Constructive and digital

Digital (44, 97, 218)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 33, 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]
2. digital (11, 64, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
      - a function field by SÃ©mirat [i]

(97−53, 97, 288)-Net in Base 32 — Constructive

(44, 97, 288)-net in base 32, using

t-expansion [i] based on (40, 97, 288)-net in base 32, using
- 11 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
  - base change [i] based on (22, 90, 288)-net in base 64, using
    - 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
      - base change [i] based on digital (9, 78, 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]

(97−53, 97, 415)-Net over F₃₂ — Digital

Digital (44, 97, 415)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−53, 97, 425)-Net in Base 32

(44, 97, 425)-net in base 32, using

11 times m-reduction [i] based on (44, 108, 425)-net in base 32, using
- base change [i] based on digital (26, 90, 425)-net over F₆₄, using
  - net from sequence [i] based on digital (26, 424)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 26 and N(F) ≥ 425, using
      - a curve from the manYPoints database [i]

(97−53, 97, 122846)-Net in Base 32 — Upper bound on s

There is no (44, 97, 122847)-net in base 32, because

1 times m-reduction [i] would yield (44, 96, 122847)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 122406 188045 900913 592047 858575 889562 776786 884628 355158 078220 925338 847118 166841 610344 753213 297514 797225 457338 831494 910737 448417 178272 492905 485545 > 32⁹⁶ [i]