MinT - Best Known (53−36, 53, s)-Nets in Base 32

Best Known (53−36, 53, s)-Nets in Base 32

(53−36, 53, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 53, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 53, 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]

(53−36, 53, 158)-Net over F₃₂ — Digital

Digital (17, 53, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 53, 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]

(53−36, 53, 177)-Net in Base 32 — Constructive

(17, 53, 177)-net in base 32, using

7 times m-reduction [i] based on (17, 60, 177)-net in base 32, using
- base change [i] based on digital (7, 50, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(53−36, 53, 6576)-Net in Base 32 — Upper bound on s

There is no (17, 53, 6577)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 59 354400 451111 450518 404722 379255 218240 955018 390940 427910 836773 974423 291655 484880 > 32⁵³ [i]