MinT - Best Known (74, 144, s)-Nets in Base 9

Best Known (74, 144, s)-Nets in Base 9

(74, 144, 232)-Net over F₉ — Constructive and digital

Digital (74, 144, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 72, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(74, 144, 302)-Net over F₉ — Digital

Digital (74, 144, 302)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 144, 14640)-Net in Base 9 — Upper bound on s

There is no (74, 144, 14641)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 257666 924607 234200 449363 297335 096251 576695 361035 725377 535962 690156 259417 748222 259758 627176 008487 187415 499738 533491 323649 214309 909289 028185 > 9¹⁴⁴ [i]