Best Known (128, 231, s)-Nets in Base 3
(128, 231, 86)-Net over F3 — Constructive and digital
Digital (128, 231, 86)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (32, 83, 38)-net over F3, using
- net from sequence [i] based on digital (32, 37)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 32 and N(F) ≥ 38, using
- net from sequence [i] based on digital (32, 37)-sequence over F3, using
- digital (45, 148, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- digital (32, 83, 38)-net over F3, using
(128, 231, 156)-Net over F3 — Digital
Digital (128, 231, 156)-net over F3, using
(128, 231, 1358)-Net in Base 3 — Upper bound on s
There is no (128, 231, 1359)-net in base 3, because
- 1 times m-reduction [i] would yield (128, 230, 1359)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 56 567198 702630 359946 621774 142293 618481 027861 939833 109309 966004 151284 631923 660491 956029 199553 667492 428215 097819 > 3230 [i]