Best Known (85, 85+43, s)-Nets in Base 3
(85, 85+43, 148)-Net over F3 — Constructive and digital
Digital (85, 128, 148)-net over F3, using
- 8 times m-reduction [i] based on digital (85, 136, 148)-net over F3, using
- trace code for nets [i] based on digital (17, 68, 74)-net over F9, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- trace code for nets [i] based on digital (17, 68, 74)-net over F9, using
(85, 85+43, 215)-Net over F3 — Digital
Digital (85, 128, 215)-net over F3, using
(85, 85+43, 3313)-Net in Base 3 — Upper bound on s
There is no (85, 128, 3314)-net in base 3, because
- 1 times m-reduction [i] would yield (85, 127, 3314)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 3 951731 353939 114149 587644 244923 717322 781233 160333 927842 176221 > 3127 [i]