Best Known (185, 225, s)-Nets in Base 3
(185, 225, 1480)-Net over F3 — Constructive and digital
Digital (185, 225, 1480)-net over F3, using
- 31 times duplication [i] based on digital (184, 224, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 56, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 56, 370)-net over F81, using
(185, 225, 4842)-Net over F3 — Digital
Digital (185, 225, 4842)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3225, 4842, F3, 40) (dual of [4842, 4617, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(3225, 6617, F3, 40) (dual of [6617, 6392, 41]-code), using
- construction X applied to Ce(39) ⊂ Ce(31) [i] based on
- linear OA(3209, 6561, F3, 40) (dual of [6561, 6352, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- 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(316, 56, F3, 7) (dual of [56, 40, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-code), using
- construction X applied to Ce(39) ⊂ Ce(31) [i] based on
- discarding factors / shortening the dual code based on linear OA(3225, 6617, F3, 40) (dual of [6617, 6392, 41]-code), using
(185, 225, 968013)-Net in Base 3 — Upper bound on s
There is no (185, 225, 968014)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 225052 080572 945606 443175 277042 286982 445579 051561 134083 579116 198368 976750 472223 946927 181414 894538 069239 573929 > 3225 [i]