MinT - Best Known (98−59, 98, s)-Nets in Base 32

Best Known (98−59, 98, s)-Nets in Base 32

(98−59, 98, 162)-Net over F₃₂ — Constructive and digital

Digital (39, 98, 162)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (3, 32, 64)-net over F₃₂, using
  - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]
2. digital (7, 66, 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]

(98−59, 98, 288)-Net in Base 32 — Constructive

(39, 98, 288)-net in base 32, using

7 times m-reduction [i] based on (39, 105, 288)-net in base 32, using
- base change [i] based on digital (9, 75, 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]

(98−59, 98, 291)-Net over F₃₂ — Digital

Digital (39, 98, 291)-net over F₃₂, using

t-expansion [i] based on digital (38, 98, 291)-net over F₃₂, using
- net from sequence [i] based on digital (38, 290)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 38 and N(F) ≥ 291, using
    - a curve from the manYPoints database [i]

(98−59, 98, 342)-Net in Base 32

(39, 98, 342)-net in base 32, using

t-expansion [i] based on (38, 98, 342)-net in base 32, using
- 10 times m-reduction [i] based on (38, 108, 342)-net in base 32, using
  - base change [i] based on digital (20, 90, 342)-net over F₆₄, using
    - net from sequence [i] based on digital (20, 341)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
        a curve from the manYPoints database [i]

(98−59, 98, 40744)-Net in Base 32 — Upper bound on s

There is no (39, 98, 40745)-net in base 32, because

1 times m-reduction [i] would yield (39, 97, 40745)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 99 935797 575882 223426 364856 478382 034931 628362 865185 717663 072766 940668 512859 438738 403908 790639 859538 460730 068632 195458 214756 523068 783941 296497 585056 > 32⁹⁷ [i]