MinT - Best Known (46, 46+47, s)-Nets in Base 32

Best Known (46, 46+47, s)-Nets in Base 32

(46, 46+47, 240)-Net over F₃₂ — Constructive and digital

Digital (46, 93, 240)-net over F₃₂, using

1 times m-reduction [i] based on digital (46, 94, 240)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 35, 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]
  2. digital (11, 59, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(46, 46+47, 513)-Net in Base 32 — Constructive

(46, 93, 513)-net in base 32, using

15 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+47, 659)-Net over F₃₂ — Digital

Digital (46, 93, 659)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 46+47, 318917)-Net in Base 32 — Upper bound on s

There is no (46, 93, 318918)-net in base 32, because

1 times m-reduction [i] would yield (46, 92, 318918)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 977213 778740 191780 395932 108451 747196 337771 145328 049774 732402 698567 604533 671658 164990 574948 244715 615434 696012 926655 773455 221177 077225 013856 > 32⁹² [i]