MinT - Best Known (76−33, 76, s)-Nets in Base 32

Best Known (76−33, 76, s)-Nets in Base 32

(76−33, 76, 240)-Net over F₃₂ — Constructive and digital

Digital (43, 76, 240)-net over F₃₂, using

9 times m-reduction [i] based on digital (43, 85, 240)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 32, 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, 53, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(76−33, 76, 513)-Net in Base 32 — Constructive

(43, 76, 513)-net in base 32, using

14 times m-reduction [i] based on (43, 90, 513)-net in base 32, using
- base change [i] based on digital (28, 75, 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]

(76−33, 76, 1566)-Net over F₃₂ — Digital

Digital (43, 76, 1566)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(76−33, 76, 2492103)-Net in Base 32 — Upper bound on s

There is no (43, 76, 2492104)-net in base 32, because

1 times m-reduction [i] would yield (43, 75, 2492104)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 76957 057698 146206 124642 672037 616549 097167 124271 397660 015907 236228 312253 879955 743877 761161 341155 899700 472311 319620 > 32⁷⁵ [i]