MinT - Best Known (110−76, 110, s)-Nets in Base 32

Best Known (110−76, 110, s)-Nets in Base 32

(110−76, 110, 120)-Net over F₃₂ — Constructive and digital

Digital (34, 110, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 110, 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]

(110−76, 110, 177)-Net in Base 32 — Constructive

(34, 110, 177)-net in base 32, using

32² times duplication [i] based on (32, 108, 177)-net in base 32, using
- t-expansion [i] based on (25, 108, 177)-net in base 32, using
  - base change [i] based on digital (7, 90, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(110−76, 110, 273)-Net over F₃₂ — Digital

Digital (34, 110, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 110, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(110−76, 110, 11007)-Net in Base 32 — Upper bound on s

There is no (34, 110, 11008)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3695 549430 028497 359453 603364 770858 089869 456167 601355 259418 053237 114941 590870 335746 554403 762187 777354 020596 453302 156493 698219 156295 875078 825380 601087 794133 413596 199993 > 32¹¹⁰ [i]