Best Known (208−82, 208, s)-Nets in Base 3
(208−82, 208, 156)-Net over F3 — Constructive and digital
Digital (126, 208, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 104, 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
(208−82, 208, 201)-Net over F3 — Digital
Digital (126, 208, 201)-net over F3, using
(208−82, 208, 2085)-Net in Base 3 — Upper bound on s
There is no (126, 208, 2086)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1775 877247 031486 811380 963735 139754 198521 610155 997241 782328 860370 178775 459283 162439 749331 823030 773117 > 3208 [i]