MinT - Best Known (29, 29+55, s)-Nets in Base 32

Best Known (29, 29+55, s)-Nets in Base 32

(29, 29+55, 120)-Net over F₃₂ — Constructive and digital

Digital (29, 84, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 84, 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+55, 216)-Net in Base 32 — Constructive

(29, 84, 216)-net in base 32, using

base change [i] based on digital (5, 60, 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]

(29, 29+55, 257)-Net over F₃₂ — Digital

Digital (29, 84, 257)-net over F₃₂, using

t-expansion [i] based on digital (28, 84, 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+55, 258)-Net in Base 32

(29, 84, 258)-net in base 32, using

base change [i] based on digital (15, 70, 258)-net over F₆₄, using
- net from sequence [i] based on digital (15, 257)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 15 and N(F) ≥ 258, using
    - a curve from the manYPoints database [i]

(29, 29+55, 14913)-Net in Base 32 — Upper bound on s

There is no (29, 84, 14914)-net in base 32, because

1 times m-reduction [i] would yield (29, 83, 14914)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 84668 777516 903040 030138 813260 392953 263261 944769 517586 041380 970993 993759 176778 708644 824776 763799 847294 124772 098795 213204 034912 > 32⁸³ [i]