MinT - Best Known (110−50, 110, s)-Nets in Base 32

Best Known (110−50, 110, s)-Nets in Base 32

(110−50, 110, 272)-Net over F₃₂ — Constructive and digital

Digital (60, 110, 272)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (5, 21, 76)-net over F₃₂, using
  - net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]
2. digital (7, 32, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]
3. digital (7, 57, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(110−50, 110, 513)-Net in Base 32 — Constructive

(60, 110, 513)-net in base 32, using

32² times duplication [i] based on (58, 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]

(110−50, 110, 1500)-Net over F₃₂ — Digital

Digital (60, 110, 1500)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(110−50, 110, 1376955)-Net in Base 32 — Upper bound on s

There is no (60, 110, 1376956)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3685 523763 052340 466738 545364 899397 359430 843612 206108 138779 656633 683959 810040 552319 372175 582225 569798 521205 970094 212138 997932 761416 520260 621706 349254 344960 025831 689155 > 32¹¹⁰ [i]