MinT - Best Known (99−56, 99, s)-Nets in Base 32

Best Known (99−56, 99, s)-Nets in Base 32

(99−56, 99, 196)-Net over F₃₂ — Constructive and digital

Digital (43, 99, 196)-net over F₃₂, using

2 times m-reduction [i] based on digital (43, 101, 196)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (7, 36, 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, 65, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(99−56, 99, 288)-Net in Base 32 — Constructive

(43, 99, 288)-net in base 32, using

t-expansion [i] based on (40, 99, 288)-net in base 32, using
- 9 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]

(99−56, 99, 344)-Net over F₃₂ — Digital

Digital (43, 99, 344)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−56, 99, 425)-Net in Base 32

(43, 99, 425)-net in base 32, using

3 times m-reduction [i] based on (43, 102, 425)-net in base 32, using
- base change [i] based on digital (26, 85, 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]

(99−56, 99, 76443)-Net in Base 32 — Upper bound on s

There is no (43, 99, 76444)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 102304 038853 511178 972883 583535 407262 551308 858003 889536 271042 472214 526005 962841 167584 778603 842618 453015 433525 570946 753418 419371 757804 521234 799729 306592 > 32⁹⁹ [i]