Best Known (120−26, 120, s)-Nets in Base 3
(120−26, 120, 600)-Net over F3 — Constructive and digital
Digital (94, 120, 600)-net over F3, using
- trace code for nets [i] based on digital (4, 30, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
(120−26, 120, 1116)-Net over F3 — Digital
Digital (94, 120, 1116)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3120, 1116, F3, 26) (dual of [1116, 996, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3120, 2187, F3, 26) (dual of [2187, 2067, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(3120, 2187, F3, 26) (dual of [2187, 2067, 27]-code), using
(120−26, 120, 71861)-Net in Base 3 — Upper bound on s
There is no (94, 120, 71862)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1797 142150 258573 088731 404761 708259 570193 129068 038869 637557 > 3120 [i]