MinT - Best Known (94−47, 94, s)-Nets in Base 32

Best Known (94−47, 94, s)-Nets in Base 32

(94−47, 94, 240)-Net over F₃₂ — Constructive and digital

Digital (47, 94, 240)-net over F₃₂, using

3 times m-reduction [i] based on digital (47, 97, 240)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 36, 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, 61, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(94−47, 94, 513)-Net in Base 32 — Constructive

(47, 94, 513)-net in base 32, using

t-expansion [i] based on (46, 94, 513)-net in base 32, using
- 14 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]

(94−47, 94, 713)-Net over F₃₂ — Digital

Digital (47, 94, 713)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(94−47, 94, 370784)-Net in Base 32 — Upper bound on s

There is no (47, 94, 370785)-net in base 32, because

1 times m-reduction [i] would yield (47, 93, 370785)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 95 268745 363088 206191 107453 150916 909959 792111 217413 189271 721136 924898 223405 414350 893519 395010 180280 812808 735267 640706 051228 781657 934572 886688 > 32⁹³ [i]