Best Known (155, 187, s)-Nets in Base 3
(155, 187, 896)-Net over F3 — Constructive and digital
Digital (155, 187, 896)-net over F3, using
- t-expansion [i] based on digital (154, 187, 896)-net over F3, using
- 1 times m-reduction [i] based on digital (154, 188, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 47, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- trace code for nets [i] based on digital (13, 47, 224)-net over F81, using
- 1 times m-reduction [i] based on digital (154, 188, 896)-net over F3, using
(155, 187, 5440)-Net over F3 — Digital
Digital (155, 187, 5440)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3187, 5440, F3, 32) (dual of [5440, 5253, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3187, 6619, F3, 32) (dual of [6619, 6432, 33]-code), using
- 3 times code embedding in larger space [i] based on linear OA(3184, 6616, F3, 32) (dual of [6616, 6432, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(24) [i] based on
- linear OA(3169, 6561, F3, 32) (dual of [6561, 6392, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3129, 6561, F3, 25) (dual of [6561, 6432, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(315, 55, F3, 6) (dual of [55, 40, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-code), using
- construction X applied to Ce(31) ⊂ Ce(24) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(3184, 6616, F3, 32) (dual of [6616, 6432, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3187, 6619, F3, 32) (dual of [6619, 6432, 33]-code), using
(155, 187, 1281911)-Net in Base 3 — Upper bound on s
There is no (155, 187, 1281912)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 166600 293767 436406 393754 696067 225606 557763 296779 293323 274780 712391 946298 951983 393371 285505 > 3187 [i]