MinT - Best Known (17, 17+51, s)-Nets in Base 32

Best Known (17, 17+51, s)-Nets in Base 32

(17, 17+51, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 68, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 68, 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]

(17, 17+51, 128)-Net in Base 32 — Constructive

(17, 68, 128)-net in base 32, using

4 times m-reduction [i] based on (17, 72, 128)-net in base 32, using
- base change [i] based on digital (5, 60, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(17, 17+51, 158)-Net over F₃₂ — Digital

Digital (17, 68, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 68, 158)-net over F₃₂, using
- net from sequence [i] based on digital (15, 157)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 15 and N(F) ≥ 158, using
    - an algebraic function field by Beelen and Pellikaan [i]

(17, 17+51, 3535)-Net in Base 32 — Upper bound on s

There is no (17, 68, 3536)-net in base 32, because

1 times m-reduction [i] would yield (17, 67, 3536)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 70052 479213 065514 143211 063769 423247 336913 851750 490716 420434 247248 024586 807258 024325 725695 762030 964708 > 32⁶⁷ [i]