MinT - Best Known (93−42, 93, s)-Nets in Base 32

Best Known (93−42, 93, s)-Nets in Base 32

(93−42, 93, 240)-Net over F₃₂ — Constructive and digital

Digital (51, 93, 240)-net over F₃₂, using

16 times m-reduction [i] based on digital (51, 109, 240)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 40, 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, 69, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(93−42, 93, 513)-Net in Base 32 — Constructive

(51, 93, 513)-net in base 32, using

t-expansion [i] based on (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]

(93−42, 93, 1372)-Net over F₃₂ — Digital

Digital (51, 93, 1372)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(93−42, 93, 1296556)-Net in Base 32 — Upper bound on s

There is no (51, 93, 1296557)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 95 268793 222467 246027 631362 465011 830717 139866 381134 763190 160028 101125 853305 244697 931807 923782 156121 862293 821417 864686 534341 996479 666866 162864 > 32⁹³ [i]