Best Known (169, 209, s)-Nets in Base 3
(169, 209, 695)-Net over F3 — Constructive and digital
Digital (169, 209, 695)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 21, 7)-net over F3, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- digital (148, 188, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 47, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 47, 172)-net over F81, using
- digital (1, 21, 7)-net over F3, using
(169, 209, 3280)-Net over F3 — Digital
Digital (169, 209, 3280)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3209, 3280, F3, 2, 40) (dual of [(3280, 2), 6351, 41]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3209, 6560, F3, 40) (dual of [6560, 6351, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(3209, 6561, F3, 40) (dual of [6561, 6352, 41]-code), using
- an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- discarding factors / shortening the dual code based on linear OA(3209, 6561, F3, 40) (dual of [6561, 6352, 41]-code), using
- OOA 2-folding [i] based on linear OA(3209, 6560, F3, 40) (dual of [6560, 6351, 41]-code), using
(169, 209, 401950)-Net in Base 3 — Upper bound on s
There is no (169, 209, 401951)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 5228 281091 266908 887770 876019 295871 635669 081910 507304 583832 888202 857041 994213 078679 788762 427595 079641 > 3209 [i]