MinT - Best Known (29, 29+79, s)-Nets in Base 32

Best Known (29, 29+79, s)-Nets in Base 32

(29, 29+79, 120)-Net over F₃₂ — Constructive and digital

Digital (29, 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]

(29, 29+79, 177)-Net in Base 32 — Constructive

(29, 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]

(29, 29+79, 257)-Net over F₃₂ — Digital

Digital (29, 108, 257)-net over F₃₂, using

t-expansion [i] based on digital (28, 108, 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]

(29, 29+79, 6672)-Net in Base 32 — Upper bound on s

There is no (29, 108, 6673)-net in base 32, because

1 times m-reduction [i] would yield (29, 107, 6673)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 113071 448363 866540 893991 354218 697001 851187 358001 652142 190455 603951 853673 463039 675670 357678 190176 557276 326924 625954 934062 338517 456613 534308 031246 673117 433133 615872 > 32¹⁰⁷ [i]