Best Known (186−61, 186, s)-Nets in Base 3
(186−61, 186, 162)-Net over F3 — Constructive and digital
Digital (125, 186, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 93, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
(186−61, 186, 315)-Net over F3 — Digital
Digital (125, 186, 315)-net over F3, using
(186−61, 186, 5242)-Net in Base 3 — Upper bound on s
There is no (125, 186, 5243)-net in base 3, because
- 1 times m-reduction [i] would yield (125, 185, 5243)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 18516 867597 197445 670575 590982 277003 544715 038212 332890 557697 504657 366639 117027 063926 280669 > 3185 [i]