Best Known (114, 114+85, s)-Nets in Base 3
(114, 114+85, 128)-Net over F3 — Constructive and digital
Digital (114, 199, 128)-net over F3, using
- 3 times m-reduction [i] based on digital (114, 202, 128)-net over F3, using
- trace code for nets [i] based on digital (13, 101, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- trace code for nets [i] based on digital (13, 101, 64)-net over F9, using
(114, 114+85, 155)-Net over F3 — Digital
Digital (114, 199, 155)-net over F3, using
(114, 114+85, 1424)-Net in Base 3 — Upper bound on s
There is no (114, 199, 1425)-net in base 3, because
- 1 times m-reduction [i] would yield (114, 198, 1425)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 29745 582023 789819 650743 238217 752995 427763 038333 913714 840014 947794 709264 641733 126067 673386 754505 > 3198 [i]