MinT - Best Known (31, 31+77, s)-Nets in Base 32

Best Known (31, 31+77, s)-Nets in Base 32

(31, 31+77, 120)-Net over F₃₂ — Constructive and digital

Digital (31, 108, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 108, 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]

(31, 31+77, 177)-Net in Base 32 — Constructive

(31, 108, 177)-net in base 32, using

t-expansion [i] based on (25, 108, 177)-net in base 32, using
- base change [i] based on digital (7, 90, 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]

(31, 31+77, 273)-Net over F₃₂ — Digital

Digital (31, 108, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 108, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(31, 31+77, 8367)-Net in Base 32 — Upper bound on s

There is no (31, 108, 8368)-net in base 32, because

1 times m-reduction [i] would yield (31, 107, 8368)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 112637 981546 812395 911507 737110 616826 406671 438159 212391 132943 709019 882198 847893 282053 959303 578474 488299 609278 644231 034246 670562 416243 684185 184063 142498 856893 892837 > 32¹⁰⁷ [i]