MinT - Best Known (29, 29+62, s)-Nets in Base 32

Best Known (29, 29+62, s)-Nets in Base 32

(29, 29+62, 120)-Net over F₃₂ — Constructive and digital

Digital (29, 91, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 91, 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]

(29, 29+62, 192)-Net in Base 32 — Constructive

(29, 91, 192)-net in base 32, using

base change [i] based on digital (3, 65, 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]

(29, 29+62, 257)-Net over F₃₂ — Digital

Digital (29, 91, 257)-net over F₃₂, using

t-expansion [i] based on digital (28, 91, 257)-net over F₃₂, using
- net from sequence [i] based on digital (28, 256)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 28 and N(F) ≥ 257, using
    - a curve from the manYPoints database [i]

(29, 29+62, 10479)-Net in Base 32 — Upper bound on s

There is no (29, 91, 10480)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 93094 161453 682712 936155 406207 615489 703387 620324 990479 203503 665968 113599 510762 104003 421091 342944 028179 225359 694106 446251 890524 244748 874362 > 32⁹¹ [i]