MinT - Best Known (15, 44, s)-Nets in Base 32

Best Known (15, 44, s)-Nets in Base 32

(15, 44, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 44, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 44, 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]

(15, 44, 158)-Net over F₃₂ — Digital

Digital (15, 44, 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]

(15, 44, 177)-Net in Base 32 — Constructive

(15, 44, 177)-net in base 32, using

4 times m-reduction [i] based on (15, 48, 177)-net in base 32, using
- base change [i] based on digital (7, 40, 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]

(15, 44, 8178)-Net in Base 32 — Upper bound on s

There is no (15, 44, 8179)-net in base 32, because

1 times m-reduction [i] would yield (15, 43, 8179)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 52677 211161 748104 946744 690393 735160 706447 706946 783280 659616 078268 > 32⁴³ [i]