MinT - Best Known (35, 35+68, s)-Nets in Base 32

Best Known (35, 35+68, s)-Nets in Base 32

(35, 35+68, 120)-Net over F₃₂ — Constructive and digital

Digital (35, 103, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 103, 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]

(35, 35+68, 216)-Net in Base 32 — Constructive

(35, 103, 216)-net in base 32, using

2 times m-reduction [i] based on (35, 105, 216)-net in base 32, using
- base change [i] based on digital (5, 75, 216)-net over F₁₂₈, using
  - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
      - a function field by SÃ©mirat [i]

(35, 35+68, 273)-Net over F₃₂ — Digital

Digital (35, 103, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 103, 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]

(35, 35+68, 15825)-Net in Base 32 — Upper bound on s

There is no (35, 103, 15826)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 107437 924056 907716 767441 767554 033342 265709 038924 260300 533044 369726 443236 196630 636105 110148 454542 508061 630646 823208 809204 245289 546522 128328 431361 720296 835920 > 32¹⁰³ [i]