Best Known (183, 183+33, s)-Nets in Base 3
(183, 183+33, 1492)-Net over F3 — Constructive and digital
Digital (183, 216, 1492)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (4, 20, 12)-net over F3, using
- net from sequence [i] based on digital (4, 11)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 4 and N(F) ≥ 12, using
- net from sequence [i] based on digital (4, 11)-sequence over F3, using
- digital (163, 196, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 49, 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, 49, 370)-net over F81, using
- digital (4, 20, 12)-net over F3, using
(183, 183+33, 12620)-Net over F3 — Digital
Digital (183, 216, 12620)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3216, 12620, F3, 33) (dual of [12620, 12404, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(3216, 19755, F3, 33) (dual of [19755, 19539, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- linear OA(3199, 19684, F3, 33) (dual of [19684, 19485, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(3145, 19684, F3, 25) (dual of [19684, 19539, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(317, 71, F3, 7) (dual of [71, 54, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3216, 19755, F3, 33) (dual of [19755, 19539, 34]-code), using
(183, 183+33, large)-Net in Base 3 — Upper bound on s
There is no (183, 216, large)-net in base 3, because
- 31 times m-reduction [i] would yield (183, 185, large)-net in base 3, but