MinT - Best Known (36, 36+48, s)-Nets in Base 32

Best Known (36, 36+48, s)-Nets in Base 32

(36, 36+48, 174)-Net over F₃₂ — Constructive and digital

Digital (36, 84, 174)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (5, 29, 76)-net over F₃₂, using
  - net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]
2. digital (7, 55, 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]

(36, 36+48, 284)-Net over F₃₂ — Digital

Digital (36, 84, 284)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(36, 36+48, 288)-Net in Base 32 — Constructive

(36, 84, 288)-net in base 32, using

t-expansion [i] based on (35, 84, 288)-net in base 32, using
- 7 times m-reduction [i] based on (35, 91, 288)-net in base 32, using
  - base change [i] based on digital (9, 65, 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]

(36, 36+48, 342)-Net in Base 32

(36, 84, 342)-net in base 32, using

12 times m-reduction [i] based on (36, 96, 342)-net in base 32, using
- base change [i] based on digital (20, 80, 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]

(36, 36+48, 58605)-Net in Base 32 — Upper bound on s

There is no (36, 84, 58606)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 708741 454089 461266 245371 382031 531583 581425 370132 585111 904017 502479 081637 217454 331103 775236 802443 182891 897853 198337 749158 668938 > 32⁸⁴ [i]