MinT - Best Known (110−54, 110, s)-Nets in Base 32

Best Known (110−54, 110, s)-Nets in Base 32

(110−54, 110, 240)-Net over F₃₂ — Constructive and digital

Digital (56, 110, 240)-net over F₃₂, using

t-expansion [i] based on digital (51, 110, 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, 70, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(110−54, 110, 513)-Net in Base 32 — Constructive

(56, 110, 513)-net in base 32, using

32² times duplication [i] based on (54, 108, 513)-net in base 32, using
- t-expansion [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]

(110−54, 110, 908)-Net over F₃₂ — Digital

Digital (56, 110, 908)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(110−54, 110, 477666)-Net in Base 32 — Upper bound on s

There is no (56, 110, 477667)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3685 571927 856859 798404 960949 923526 845061 909481 100049 700860 001226 458606 100182 654835 282529 954922 521612 599088 475378 871401 251998 518117 718679 341717 739698 744851 390165 997344 > 32¹¹⁰ [i]