MinT - Best Known (51−35, 51, s)-Nets in Base 32

Best Known (51−35, 51, s)-Nets in Base 32

(51−35, 51, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 51, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 51, 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]

(51−35, 51, 158)-Net over F₃₂ — Digital

Digital (16, 51, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 51, 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]

(51−35, 51, 177)-Net in Base 32 — Constructive

(16, 51, 177)-net in base 32, using

3 times m-reduction [i] based on (16, 54, 177)-net in base 32, using
- base change [i] based on digital (7, 45, 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]

(51−35, 51, 6178)-Net in Base 32 — Upper bound on s

There is no (16, 51, 6179)-net in base 32, because

1 times m-reduction [i] would yield (16, 50, 6179)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1810 895678 361884 696362 287532 777995 566050 073383 721074 099510 301442 915457 298932 > 32⁵⁰ [i]