MinT - Best Known (66−28, 66, s)-Nets in Base 32

Best Known (66−28, 66, s)-Nets in Base 32

(66−28, 66, 240)-Net over F₃₂ — Constructive and digital

Digital (38, 66, 240)-net over F₃₂, using

4 times m-reduction [i] based on digital (38, 70, 240)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 27, 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]
  2. digital (11, 43, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(66−28, 66, 386)-Net in Base 32 — Constructive

(38, 66, 386)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (6, 20, 129)-net in base 32, using
  - 1 times m-reduction [i] based on (6, 21, 129)-net in base 32, using
    - base change [i] based on digital (0, 15, 129)-net over F₁₂₈, using
      - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
        the rational function field F₁₂₈(x) [i]
        Niederreiter sequence [i]
2. (18, 46, 257)-net in base 32, using
  - 2 times m-reduction [i] based on (18, 48, 257)-net in base 32, using
    - base change [i] based on digital (0, 30, 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]

(66−28, 66, 1697)-Net over F₃₂ — Digital

Digital (38, 66, 1697)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(66−28, 66, 2431094)-Net in Base 32 — Upper bound on s

There is no (38, 66, 2431095)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2187 256768 248268 482910 324764 296086 008535 716293 847879 755830 480706 331026 049378 864070 712151 319130 537334 > 32⁶⁶ [i]