MinT - Best Known (99, 99+73, s)-Nets in Base 3

Best Known (99, 99+73, s)-Nets in Base 3

(99, 99+73, 128)-Net over F₃ — Constructive and digital

Digital (99, 172, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 86, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(99, 99+73, 139)-Net over F₃ — Digital

Digital (99, 172, 139)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+73, 1283)-Net in Base 3 — Upper bound on s

There is no (99, 172, 1284)-net in base 3, because

1 times m-reduction [i] would yield (99, 171, 1284)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3950 247935 858511 709793 018684 790488 798740 035232 701175 890393 281493 228035 412572 726465 > 3¹⁷¹ [i]