MinT - Best Known (62, 62+42, s)-Nets in Base 32

Best Known (62, 62+42, s)-Nets in Base 32

(62, 62+42, 322)-Net over F₃₂ — Constructive and digital

Digital (62, 104, 322)-net over F₃₂, using

1 times m-reduction [i] based on digital (62, 105, 322)-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 (9, 30, 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]
  3. digital (11, 54, 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]

(62, 62+42, 516)-Net in Base 32 — Constructive

(62, 104, 516)-net in base 32, using

base change [i] based on digital (23, 65, 516)-net over F₂₅₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 22, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
  2. digital (1, 43, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(62, 62+42, 3444)-Net over F₃₂ — Digital

Digital (62, 104, 3444)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+42, 7965377)-Net in Base 32 — Upper bound on s

There is no (62, 104, 7965378)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 432401 469369 636017 755199 363694 664670 324957 147245 827074 120400 966740 210293 122928 022349 667579 043460 177202 802583 416479 774786 868441 337292 345678 429958 237071 729264 > 32¹⁰⁴ [i]