MinT - Best Known (104−70, 104, s)-Nets in Base 32

Best Known (104−70, 104, s)-Nets in Base 32

(104−70, 104, 120)-Net over F₃₂ — Constructive and digital

Digital (34, 104, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 104, 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]

(104−70, 104, 192)-Net in Base 32 — Constructive

(34, 104, 192)-net in base 32, using

4 times m-reduction [i] based on (34, 108, 192)-net in base 32, using
- base change [i] based on (16, 90, 192)-net in base 64, using
  - 1 times m-reduction [i] based on (16, 91, 192)-net in base 64, using
    - base change [i] based on digital (3, 78, 192)-net over F₁₂₈, using
      - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(104−70, 104, 273)-Net over F₃₂ — Digital

Digital (34, 104, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 104, 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]

(104−70, 104, 13297)-Net in Base 32 — Upper bound on s

There is no (34, 104, 13298)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 440728 339604 199971 793055 656144 704892 067812 542768 193975 791161 090724 403141 011551 467172 014669 560410 495173 402574 475993 152197 037842 387104 741875 071336 230188 399448 > 32¹⁰⁴ [i]