MinT - Best Known (66−49, 66, s)-Nets in Base 32

Best Known (66−49, 66, s)-Nets in Base 32

(66−49, 66, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 66, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 66, 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]

(66−49, 66, 128)-Net in Base 32 — Constructive

(17, 66, 128)-net in base 32, using

6 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]

(66−49, 66, 158)-Net over F₃₂ — Digital

Digital (17, 66, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 66, 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]

(66−49, 66, 161)-Net in Base 32

(17, 66, 161)-net in base 32, using

base change [i] based on digital (6, 55, 161)-net over F₆₄, using
- net from sequence [i] based on digital (6, 160)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 6 and N(F) ≥ 161, using
    - a curve from the manYPoints database [i]

(66−49, 66, 3758)-Net in Base 32 — Upper bound on s

There is no (17, 66, 3759)-net in base 32, because

1 times m-reduction [i] would yield (17, 65, 3759)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 68 496018 096860 411401 851177 694101 532468 589165 014691 869671 124887 261288 966110 953407 105304 806972 148406 > 32⁶⁵ [i]