MinT - Best Known (15, 76, s)-Nets in Base 128

Best Known (15, 76, s)-Nets in Base 128

(15, 76, 288)-Net over F₁₂₈ — Constructive and digital

Digital (15, 76, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 76, 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, 76, 386)-Net over F₁₂₈ — Digital

Digital (15, 76, 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, 76, 17564)-Net in Base 128 — Upper bound on s

There is no (15, 76, 17565)-net in base 128, because

1 times m-reduction [i] would yield (15, 75, 17565)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 109 855159 336624 862926 011170 964883 453877 731426 944560 004966 710214 220365 653540 348375 592342 599660 939496 392008 360387 229717 794243 719360 033636 921571 790401 103590 380864 > 128⁷⁵ [i]