MinT - Best Known (9, 9+68, s)-Nets in Base 128

Best Known (9, 9+68, s)-Nets in Base 128

(9, 9+68, 288)-Net over F₁₂₈ — Constructive and digital

Digital (9, 77, 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]

(9, 9+68, 6291)-Net in Base 128 — Upper bound on s

There is no (9, 77, 6292)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 1 808242 510402 412707 813386 435373 443244 380937 233258 118051 372974 159706 799443 583092 144938 463534 293144 157785 653620 719039 736077 323198 930737 874164 377257 400161 207508 209660 > 128⁷⁷ [i]