MinT - Best Known (62, 62+48, s)-Nets in Base 32

Best Known (62, 62+48, s)-Nets in Base 32

(62, 62+48, 294)-Net over F₃₂ — Constructive and digital

Digital (62, 110, 294)-net over F₃₂, using

t-expansion [i] based on digital (61, 110, 294)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 23, 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, 31, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  3. digital (7, 56, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(62, 62+48, 513)-Net in Base 32 — Constructive

(62, 110, 513)-net in base 32, using

32² times duplication [i] based on (60, 108, 513)-net in base 32, using
- t-expansion [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]

(62, 62+48, 1998)-Net over F₃₂ — Digital

Digital (62, 110, 1998)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+48, 2503819)-Net in Base 32 — Upper bound on s

There is no (62, 110, 2503820)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3685 535318 899029 687593 900607 519572 151669 523581 468274 789478 192720 717055 887508 660444 480207 447288 413731 574727 024993 568747 094532 935560 611220 390630 105378 845065 150737 788712 > 32¹¹⁰ [i]