MinT - Best Known (44, 44+61, s)-Nets in Base 32

Best Known (44, 44+61, s)-Nets in Base 32

(44, 44+61, 196)-Net over F₃₂ — Constructive and digital

Digital (44, 105, 196)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 37, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]
2. digital (7, 68, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(44, 44+61, 288)-Net in Base 32 — Constructive

(44, 105, 288)-net in base 32, using

t-expansion [i] based on (40, 105, 288)-net in base 32, using
- 3 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
  - base change [i] based on (22, 90, 288)-net in base 64, using
    - 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
      - base change [i] based on digital (9, 78, 288)-net over F₁₂₈, using
        net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(44, 44+61, 325)-Net over F₃₂ — Digital

Digital (44, 105, 325)-net over F₃₂, using

net from sequence [i] based on digital (44, 324)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 44 and N(F) ≥ 325, using
  - a curve from the manYPoints database [i]

(44, 44+61, 425)-Net in Base 32

(44, 105, 425)-net in base 32, using

3 times m-reduction [i] based on (44, 108, 425)-net in base 32, using
- base change [i] based on digital (26, 90, 425)-net over F₆₄, using
  - net from sequence [i] based on digital (26, 424)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 26 and N(F) ≥ 425, using
      - a curve from the manYPoints database [i]

(44, 44+61, 64146)-Net in Base 32 — Upper bound on s

There is no (44, 105, 64147)-net in base 32, because

1 times m-reduction [i] would yield (44, 104, 64147)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 432593 244686 368387 960628 194462 042397 534867 308736 188888 528574 899569 566159 662324 322816 212308 151247 276479 630414 972974 817307 590064 579004 715765 522980 532495 056672 > 32¹⁰⁴ [i]