Best Known (200, 247, s)-Nets in Base 3
(200, 247, 896)-Net over F3 — Constructive and digital
Digital (200, 247, 896)-net over F3, using
- t-expansion [i] based on digital (199, 247, 896)-net over F3, using
- 1 times m-reduction [i] based on digital (199, 248, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 62, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- trace code for nets [i] based on digital (13, 62, 224)-net over F81, using
- 1 times m-reduction [i] based on digital (199, 248, 896)-net over F3, using
(200, 247, 3343)-Net over F3 — Digital
Digital (200, 247, 3343)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3247, 3343, F3, 47) (dual of [3343, 3096, 48]-code), using
- 52 step Varšamov–Edel lengthening with (ri) = (1, 16 times 0, 1, 34 times 0) [i] based on linear OA(3245, 3289, F3, 47) (dual of [3289, 3044, 48]-code), using
- construction X applied to Ce(46) ⊂ Ce(45) [i] based on
- linear OA(3245, 3281, F3, 47) (dual of [3281, 3036, 48]-code), using an extension Ce(46) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(3237, 3281, F3, 46) (dual of [3281, 3044, 47]-code), using an extension Ce(45) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(30, 8, F3, 0) (dual of [8, 8, 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 X applied to Ce(46) ⊂ Ce(45) [i] based on
- 52 step Varšamov–Edel lengthening with (ri) = (1, 16 times 0, 1, 34 times 0) [i] based on linear OA(3245, 3289, F3, 47) (dual of [3289, 3044, 48]-code), using
(200, 247, 597768)-Net in Base 3 — Upper bound on s
There is no (200, 247, 597769)-net in base 3, because
- 1 times m-reduction [i] would yield (200, 246, 597769)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 2354 178465 158783 878186 416774 455851 871661 851187 896870 563846 707846 216977 269777 524504 499656 846296 518135 826460 184185 004395 > 3246 [i]