MinT - Best Known (62, 62+43, s)-Nets in Base 32

Best Known (62, 62+43, s)-Nets in Base 32

(62, 62+43, 322)-Net over F₃₂ — Constructive and digital

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+43, 515)-Net in Base 32 — Constructive

(62, 105, 515)-net in base 32, using

32¹ times duplication [i] based on (61, 104, 515)-net in base 32, using
- base change [i] based on digital (22, 65, 515)-net over F₂₅₆, using
  - (u,Â u+v)-construction [i] based on
    1. digital (0, 21, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]
    2. digital (1, 44, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(62, 62+43, 3106)-Net over F₃₂ — Digital

Digital (62, 105, 3106)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+43, 7965377)-Net in Base 32 — Upper bound on s

There is no (62, 105, 7965378)-net in base 32, because

1 times m-reduction [i] would yield (62, 104, 7965378)-net in base 32, but
- 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]