Best Known (119, 151, s)-Nets in Base 3
(119, 151, 640)-Net over F3 — Constructive and digital
Digital (119, 151, 640)-net over F3, using
- 1 times m-reduction [i] based on digital (119, 152, 640)-net over F3, using
- trace code for nets [i] based on digital (5, 38, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- trace code for nets [i] based on digital (5, 38, 160)-net over F81, using
(119, 151, 1436)-Net over F3 — Digital
Digital (119, 151, 1436)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3151, 1436, F3, 32) (dual of [1436, 1285, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3151, 2200, F3, 32) (dual of [2200, 2049, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(28) [i] based on
- linear OA(3148, 2187, F3, 32) (dual of [2187, 2039, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3134, 2187, F3, 29) (dual of [2187, 2053, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- construction X applied to Ce(31) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(3151, 2200, F3, 32) (dual of [2200, 2049, 33]-code), using
(119, 151, 108212)-Net in Base 3 — Upper bound on s
There is no (119, 151, 108213)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1 110009 017296 671973 375160 342753 999581 944816 670824 778846 942017 216217 075137 > 3151 [i]