Best Known (153−83, 153, s)-Nets in Base 3
(153−83, 153, 52)-Net over F3 — Constructive and digital
Digital (70, 153, 52)-net over F3, using
- 1 times m-reduction [i] based on digital (70, 154, 52)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (13, 55, 24)-net over F3, using
- net from sequence [i] based on digital (13, 23)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 13 and N(F) ≥ 24, using
- net from sequence [i] based on digital (13, 23)-sequence over F3, using
- digital (15, 99, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- digital (13, 55, 24)-net over F3, using
- (u, u+v)-construction [i] based on
(153−83, 153, 82)-Net over F3 — Digital
Digital (70, 153, 82)-net over F3, using
- t-expansion [i] based on digital (69, 153, 82)-net over F3, using
- net from sequence [i] based on digital (69, 81)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 69 and N(F) ≥ 82, using
- net from sequence [i] based on digital (69, 81)-sequence over F3, using
(153−83, 153, 434)-Net in Base 3 — Upper bound on s
There is no (70, 153, 435)-net in base 3, because
- 1 times m-reduction [i] would yield (70, 152, 435)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 3 382628 804145 737445 334527 981359 135753 222641 895891 682483 947239 097142 153687 > 3152 [i]