Best Known (60, 80, s)-Nets in Base 3
(60, 80, 328)-Net over F3 — Constructive and digital
Digital (60, 80, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 20, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
(60, 80, 453)-Net over F3 — Digital
Digital (60, 80, 453)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(380, 453, F3, 20) (dual of [453, 373, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(380, 741, F3, 20) (dual of [741, 661, 21]-code), using
- construction XX applied to C1 = C([346,364]), C2 = C([348,365]), C3 = C1 + C2 = C([348,364]), and C∩ = C1 ∩ C2 = C([346,365]) [i] based on
- linear OA(373, 728, F3, 19) (dual of [728, 655, 20]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {346,347,…,364}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(373, 728, F3, 18) (dual of [728, 655, 19]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {348,349,…,365}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(379, 728, F3, 20) (dual of [728, 649, 21]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {346,347,…,365}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(367, 728, F3, 17) (dual of [728, 661, 18]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {348,349,…,364}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction XX applied to C1 = C([346,364]), C2 = C([348,365]), C3 = C1 + C2 = C([348,364]), and C∩ = C1 ∩ C2 = C([346,365]) [i] based on
- discarding factors / shortening the dual code based on linear OA(380, 741, F3, 20) (dual of [741, 661, 21]-code), using
(60, 80, 14846)-Net in Base 3 — Upper bound on s
There is no (60, 80, 14847)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 147 809126 898682 905503 012055 485784 028141 > 380 [i]