MinT - Best Known (10, 10+26, s)-Nets in Base 32

Best Known (10, 10+26, s)-Nets in Base 32

(10, 10+26, 104)-Net over F₃₂ — Constructive and digital

Digital (10, 36, 104)-net over F₃₂, using

t-expansion [i] based on digital (9, 36, 104)-net over F₃₂, using
- net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(10, 10+26, 113)-Net over F₃₂ — Digital

Digital (10, 36, 113)-net over F₃₂, using

net from sequence [i] based on digital (10, 112)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 10 and N(F) ≥ 113, using
  - a curve from the manYPoints database [i]

(10, 10+26, 129)-Net in Base 32

(10, 36, 129)-net in base 32, using

base change [i] based on digital (4, 30, 129)-net over F₆₄, using
- net from sequence [i] based on digital (4, 128)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 4 and N(F) ≥ 129, using
    - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]

(10, 10+26, 2686)-Net in Base 32 — Upper bound on s

There is no (10, 36, 2687)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 539451 224427 188985 533647 122947 476247 199474 234669 163790 > 32³⁶ [i]