Best Known (121, 121+118, s)-Nets in Base 3
(121, 121+118, 78)-Net over F3 — Constructive and digital
Digital (121, 239, 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+118, 121)-Net over F3 — Digital
Digital (121, 239, 121)-net over F3, using
(121, 121+118, 920)-Net in Base 3 — Upper bound on s
There is no (121, 239, 921)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1 124710 903648 908005 873070 234065 601141 934016 312507 922166 400030 013039 080606 294211 037337 985705 397852 623729 030507 115611 > 3239 [i]