Best Known (137, 137+73, s)-Nets in Base 3
(137, 137+73, 162)-Net over F3 — Constructive and digital
Digital (137, 210, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 105, 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
(137, 137+73, 292)-Net over F3 — Digital
Digital (137, 210, 292)-net over F3, using
(137, 137+73, 4168)-Net in Base 3 — Upper bound on s
There is no (137, 210, 4169)-net in base 3, because
- 1 times m-reduction [i] would yield (137, 209, 4169)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 5245 635915 983371 581956 115793 858538 668056 391105 329086 658425 331232 667197 095185 831314 780336 313029 094545 > 3209 [i]