MinT - Best Known (59, 59+42, s)-Nets in Base 32

Best Known (59, 59+42, s)-Nets in Base 32

(59, 59+42, 300)-Net over F₃₂ — Constructive and digital

Digital (59, 101, 300)-net over F₃₂, using

2 times m-reduction [i] based on digital (59, 103, 300)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 21, 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 (7, 29, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  3. digital (9, 53, 104)-net over F₃₂, using
    - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]

(59, 59+42, 513)-Net in Base 32 — Constructive

(59, 101, 513)-net in base 32, using

t-expansion [i] based on (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]

(59, 59+42, 2677)-Net over F₃₂ — Digital

Digital (59, 101, 2677)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+42, 4854947)-Net in Base 32 — Upper bound on s

There is no (59, 101, 4854948)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 104 748533 785728 331085 756103 576291 535246 072830 590368 595122 551507 472784 711133 713784 512184 653492 170894 465358 464703 248904 814236 379444 686555 724454 078016 071224 > 32¹⁰¹ [i]