MinT - Best Known (16, 74, s)-Nets in Base 128

Best Known (16, 74, s)-Nets in Base 128

(16, 74, 288)-Net over F₁₂₈ — Constructive and digital

Digital (16, 74, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 74, 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, 74, 386)-Net over F₁₂₈ — Digital

Digital (16, 74, 386)-net over F₁₂₈, using

t-expansion [i] based on digital (15, 74, 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, 74, 21880)-Net in Base 128 — Upper bound on s

There is no (16, 74, 21881)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 858821 621314 878618 001072 742007 622247 726615 044577 786404 420151 226179 937546 393010 965222 316798 853889 236184 843551 425866 061973 077674 583662 708741 616812 634013 231008 > 128⁷⁴ [i]