MinT - Best Known (109−80, 109, s)-Nets in Base 32

Best Known (109−80, 109, s)-Nets in Base 32

(109−80, 109, 120)-Net over F₃₂ — Constructive and digital

Digital (29, 109, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 109, 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]

(109−80, 109, 177)-Net in Base 32 — Constructive

(29, 109, 177)-net in base 32, using

32¹ times duplication [i] based on (28, 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]

(109−80, 109, 257)-Net over F₃₂ — Digital

Digital (29, 109, 257)-net over F₃₂, using

t-expansion [i] based on digital (28, 109, 257)-net over F₃₂, using
- net from sequence [i] based on digital (28, 256)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 28 and N(F) ≥ 257, using
    - a curve from the manYPoints database [i]

(109−80, 109, 6405)-Net in Base 32 — Upper bound on s

There is no (29, 109, 6406)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 115 491229 457351 092238 613764 787671 209959 455312 792973 975872 777495 567453 137538 642100 926221 900131 696448 739091 999591 596522 973047 567639 197172 736565 388330 169042 891440 590880 > 32¹⁰⁹ [i]