MinT - Best Known (16, 67, s)-Nets in Base 128

Best Known (16, 67, s)-Nets in Base 128

(16, 67, 288)-Net over F₁₂₈ — Constructive and digital

Digital (16, 67, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 67, 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]

(16, 67, 386)-Net over F₁₂₈ — Digital

Digital (16, 67, 386)-net over F₁₂₈, using

t-expansion [i] based on digital (15, 67, 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]

(16, 67, 29287)-Net in Base 128 — Upper bound on s

There is no (16, 67, 29288)-net in base 128, because

1 times m-reduction [i] would yield (16, 66, 29288)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 11 918193 695146 336304 639080 014150 298903 683632 827826 446471 539642 019413 470741 492112 405855 694496 670765 184677 193340 051623 397516 526292 514045 979180 > 128⁶⁶ [i]