Best Known (215−76, 215, s)-Nets in Base 3
(215−76, 215, 156)-Net over F3 — Constructive and digital
Digital (139, 215, 156)-net over F3, using
- 19 times m-reduction [i] based on digital (139, 234, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 117, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- trace code for nets [i] based on digital (22, 117, 78)-net over F9, using
(215−76, 215, 284)-Net over F3 — Digital
Digital (139, 215, 284)-net over F3, using
(215−76, 215, 3723)-Net in Base 3 — Upper bound on s
There is no (139, 215, 3724)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 3 834057 410578 741944 000759 537192 696358 542179 313673 030958 926001 294728 916867 620876 738696 209950 610691 535625 > 3215 [i]