MinT - Best Known (48, 48+59, s)-Nets in Base 32

Best Known (48, 48+59, s)-Nets in Base 32

(48, 48+59, 218)-Net over F₃₂ — Constructive and digital

Digital (48, 107, 218)-net over F₃₂, using

1 times m-reduction [i] based on digital (48, 108, 218)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (7, 37, 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 (11, 71, 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]

(48, 48+59, 425)-Net over F₃₂ — Digital

Digital (48, 107, 425)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 48+59, 513)-Net in Base 32 — Constructive

(48, 107, 513)-net in base 32, using

t-expansion [i] based on (46, 107, 513)-net in base 32, using
- 1 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]

(48, 48+59, 119478)-Net in Base 32 — Upper bound on s

There is no (48, 107, 119479)-net in base 32, because

1 times m-reduction [i] would yield (48, 106, 119479)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3515 445211 302075 013512 818880 532354 750941 777488 111692 762423 290497 765283 025997 538995 355499 609285 078710 659330 334154 149474 664091 925815 899234 683002 781821 371297 589192 > 32¹⁰⁶ [i]