MinT - Best Known (58, 58+44, s)-Nets in Base 32

Best Known (58, 58+44, s)-Nets in Base 32

(58, 58+44, 294)-Net over F₃₂ — Constructive and digital

Digital (58, 102, 294)-net over F₃₂, using

1 times m-reduction [i] based on digital (58, 103, 294)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 22, 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 (7, 52, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(58, 58+44, 513)-Net in Base 32 — Constructive

(58, 102, 513)-net in base 32, using

t-expansion [i] based on (46, 102, 513)-net in base 32, using
- 6 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]

(58, 58+44, 2047)-Net over F₃₂ — Digital

Digital (58, 102, 2047)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+44, 2779151)-Net in Base 32 — Upper bound on s

There is no (58, 102, 2779152)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3351 967627 193480 239309 829255 856595 671015 666652 303022 222717 168811 702275 674493 218421 662153 046517 884973 132033 421281 602161 591926 485407 997548 613767 540853 324928 > 32¹⁰² [i]