Best Known (150, 184, s)-Nets in Base 3
(150, 184, 698)-Net over F3 — Constructive and digital
Digital (150, 184, 698)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (3, 20, 10)-net over F3, using
- net from sequence [i] based on digital (3, 9)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 3 and N(F) ≥ 10, using
- net from sequence [i] based on digital (3, 9)-sequence over F3, using
- digital (130, 164, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 41, 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, 41, 172)-net over F81, using
- digital (3, 20, 10)-net over F3, using
(150, 184, 3393)-Net over F3 — Digital
Digital (150, 184, 3393)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3184, 3393, F3, 34) (dual of [3393, 3209, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3184, 6588, F3, 34) (dual of [6588, 6404, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(28) [i] based on
- linear OA(3177, 6561, F3, 34) (dual of [6561, 6384, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3153, 6561, F3, 29) (dual of [6561, 6408, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(37, 27, F3, 4) (dual of [27, 20, 5]-code), using
- an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- construction X applied to Ce(33) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(3184, 6588, F3, 34) (dual of [6588, 6404, 35]-code), using
(150, 184, 523645)-Net in Base 3 — Upper bound on s
There is no (150, 184, 523646)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 6170 444903 264727 198924 994465 897624 348746 598087 537947 931102 125208 294772 426069 371012 799709 > 3184 [i]