MinT - Best Known (46, 46+53, s)-Nets in Base 32

Best Known (46, 46+53, s)-Nets in Base 32

(46, 46+53, 224)-Net over F₃₂ — Constructive and digital

Digital (46, 99, 224)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (9, 35, 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]
2. digital (11, 64, 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]

(46, 46+53, 478)-Net over F₃₂ — Digital

Digital (46, 99, 478)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 46+53, 513)-Net in Base 32 — Constructive

(46, 99, 513)-net in base 32, using

9 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]

(46, 46+53, 160380)-Net in Base 32 — Upper bound on s

There is no (46, 99, 160381)-net in base 32, because

1 times m-reduction [i] would yield (46, 98, 160381)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3196 685523 759764 735835 336467 467466 437951 346222 483367 322672 806736 931100 937823 961354 173153 523350 677200 679000 956955 990890 563381 370269 218020 353872 556374 > 32⁹⁸ [i]