MinT - Best Known (24, 24+40, s)-Nets in Base 128

Best Known (24, 24+40, s)-Nets in Base 128

(24, 24+40, 342)-Net over F₁₂₈ — Constructive and digital

Digital (24, 64, 342)-net over F₁₂₈, using

(u,Â u+v)-construction [i] based on
1. digital (1, 21, 150)-net over F₁₂₈, using
  - net from sequence [i] based on digital (1, 149)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]
2. digital (3, 43, 192)-net over F₁₂₈, using
  - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]

(24, 24+40, 513)-Net over F₁₂₈ — Digital

Digital (24, 64, 513)-net over F₁₂₈, using

net from sequence [i] based on digital (24, 512)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 24 and N(F) ≥ 513, using
  - a curve from the manYPoints database [i]

(24, 24+40, 361878)-Net in Base 128 — Upper bound on s

There is no (24, 64, 361879)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 726 857421 955787 428826 923816 644653 883274 625045 267272 771084 151790 758674 612117 099090 610804 852631 621317 784850 380606 497752 152752 294295 068671 > 128⁶⁴ [i]