Best Known (121, 121+116, s)-Nets in Base 3
(121, 121+116, 78)-Net over F3 — Constructive and digital
Digital (121, 237, 78)-net over F3, using
- net from sequence [i] based on digital (121, 77)-sequence over F3, using
- base reduction for sequences [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
- base reduction for sequences [i] based on digital (22, 77)-sequence over F9, using
(121, 121+116, 123)-Net over F3 — Digital
Digital (121, 237, 123)-net over F3, using
(121, 121+116, 943)-Net in Base 3 — Upper bound on s
There is no (121, 237, 944)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 123794 728791 713350 988613 152027 650907 085900 305460 067810 404503 505831 623341 228987 059827 009591 028478 150501 505101 039905 > 3237 [i]