Best Known (128, 128+84, s)-Nets in Base 3
(128, 128+84, 156)-Net over F3 — Constructive and digital
Digital (128, 212, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 106, 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
(128, 128+84, 202)-Net over F3 — Digital
Digital (128, 212, 202)-net over F3, using
(128, 128+84, 2072)-Net in Base 3 — Upper bound on s
There is no (128, 212, 2073)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 141710 614178 187390 028927 727791 098611 658732 145880 022658 757980 517661 860257 131028 544745 327097 309398 262809 > 3212 [i]