MinT - Best Known (101−55, 101, s)-Nets in Base 32

Best Known (101−55, 101, s)-Nets in Base 32

(101−55, 101, 218)-Net over F₃₂ — Constructive and digital

Digital (46, 101, 218)-net over F₃₂, using

1 times m-reduction [i] based on digital (46, 102, 218)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (7, 35, 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, 67, 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]

(101−55, 101, 438)-Net over F₃₂ — Digital

Digital (46, 101, 438)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(101−55, 101, 513)-Net in Base 32 — Constructive

(46, 101, 513)-net in base 32, using

7 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
- base change [i] based on digital (28, 90, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(101−55, 101, 132321)-Net in Base 32 — Upper bound on s

There is no (46, 101, 132322)-net in base 32, because

1 times m-reduction [i] would yield (46, 100, 132322)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 273991 708425 667386 111831 810246 245088 906890 080206 478040 882461 677427 016302 910259 312785 367490 357178 539578 707462 101200 052676 820540 046171 686849 416681 720112 > 32¹⁰⁰ [i]