MinT - Best Known (30, 30+71, s)-Nets in Base 32

Best Known (30, 30+71, s)-Nets in Base 32

(30, 30+71, 120)-Net over F₃₂ — Constructive and digital

Digital (30, 101, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 101, 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]

(30, 30+71, 177)-Net in Base 32 — Constructive

(30, 101, 177)-net in base 32, using

t-expansion [i] based on (25, 101, 177)-net in base 32, using
- 7 times m-reduction [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]

(30, 30+71, 273)-Net over F₃₂ — Digital

Digital (30, 101, 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]

(30, 30+71, 8942)-Net in Base 32 — Upper bound on s

There is no (30, 101, 8943)-net in base 32, because

1 times m-reduction [i] would yield (30, 100, 8943)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 281775 098690 643217 411639 928895 729985 789687 260278 511132 551455 329853 359078 826154 788668 640188 115802 943327 787303 996780 383262 462673 835974 803365 057495 736236 > 32¹⁰⁰ [i]