Best Known (78, 78+117, s)-Nets in Base 3
(78, 78+117, 53)-Net over F3 — Constructive and digital
Digital (78, 195, 53)-net over F3, using
- net from sequence [i] based on digital (78, 52)-sequence over F3, using
- base reduction for sequences [i] based on digital (13, 52)-sequence over F9, using
- s-reduction 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
- s-reduction based on digital (13, 63)-sequence over F9, using
- base reduction for sequences [i] based on digital (13, 52)-sequence over F9, using
(78, 78+117, 84)-Net over F3 — Digital
Digital (78, 195, 84)-net over F3, using
- t-expansion [i] based on digital (71, 195, 84)-net over F3, using
- net from sequence [i] based on digital (71, 83)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 71 and N(F) ≥ 84, using
- net from sequence [i] based on digital (71, 83)-sequence over F3, using
(78, 78+117, 388)-Net in Base 3 — Upper bound on s
There is no (78, 195, 389)-net in base 3, because
- 1 times m-reduction [i] would yield (78, 194, 389)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 411 125298 442244 647199 852586 252914 092793 219962 134080 103365 683858 213689 191011 658691 784022 009265 > 3194 [i]