MinT - Best Known (28, 28+20, s)-Nets in Base 32

Best Known (28, 28+20, s)-Nets in Base 32

(28, 28+20, 218)-Net over F₃₂ — Constructive and digital

Digital (28, 48, 218)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 17, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]
2. digital (11, 31, 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]

(28, 28+20, 514)-Net in Base 32 — Constructive

(28, 48, 514)-net in base 32, using

base change [i] based on digital (10, 30, 514)-net over F₂₅₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 10, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
      - Niederreiter sequence [i]
  2. digital (0, 20, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(28, 28+20, 1633)-Net over F₃₂ — Digital

Digital (28, 48, 1633)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(28, 28+20, 2450945)-Net in Base 32 — Upper bound on s

There is no (28, 48, 2450946)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 766850 807323 958964 703620 239410 350207 770024 077877 977168 481184 154849 595136 > 32⁴⁸ [i]