MinT - Best Known (15, 72, s)-Nets in Base 128

Best Known (15, 72, s)-Nets in Base 128

(15, 72, 288)-Net over F₁₂₈ — Constructive and digital

Digital (15, 72, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 72, 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]

(15, 72, 386)-Net over F₁₂₈ — Digital

Digital (15, 72, 386)-net over F₁₂₈, using

net from sequence [i] based on digital (15, 385)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 15 and N(F) ≥ 386, using
  - a curve from the manYPoints database [i]

(15, 72, 19596)-Net in Base 128 — Upper bound on s

There is no (15, 72, 19597)-net in base 128, because

1 times m-reduction [i] would yield (15, 71, 19597)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 409431 847073 529088 872758 191905 843960 011918 080194 584762 143707 844101 255673 349514 821304 827882 676630 981396 860730 516939 726153 789578 817399 150195 470302 948904 > 128⁷¹ [i]