Best Known (203, 203+34, s)-Nets in Base 3
(203, 203+34, 3477)-Net over F3 — Constructive and digital
Digital (203, 237, 3477)-net over F3, using
- net defined by OOA [i] based on linear OOA(3237, 3477, F3, 34, 34) (dual of [(3477, 34), 117981, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(3237, 59109, F3, 34) (dual of [59109, 58872, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3237, 59115, F3, 34) (dual of [59115, 58878, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(25) [i] based on
- linear OA(3221, 59049, F3, 34) (dual of [59049, 58828, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(316, 66, F3, 7) (dual of [66, 50, 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(33) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3237, 59115, F3, 34) (dual of [59115, 58878, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(3237, 59109, F3, 34) (dual of [59109, 58872, 35]-code), using
(203, 203+34, 25667)-Net over F3 — Digital
Digital (203, 237, 25667)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3237, 25667, F3, 2, 34) (dual of [(25667, 2), 51097, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3237, 29557, F3, 2, 34) (dual of [(29557, 2), 58877, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3237, 59114, F3, 34) (dual of [59114, 58877, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3237, 59115, F3, 34) (dual of [59115, 58878, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(25) [i] based on
- linear OA(3221, 59049, F3, 34) (dual of [59049, 58828, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(316, 66, F3, 7) (dual of [66, 50, 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(33) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3237, 59115, F3, 34) (dual of [59115, 58878, 35]-code), using
- OOA 2-folding [i] based on linear OA(3237, 59114, F3, 34) (dual of [59114, 58877, 35]-code), using
- discarding factors / shortening the dual code based on linear OOA(3237, 29557, F3, 2, 34) (dual of [(29557, 2), 58877, 35]-NRT-code), using
(203, 203+34, large)-Net in Base 3 — Upper bound on s
There is no (203, 237, large)-net in base 3, because
- 32 times m-reduction [i] would yield (203, 205, large)-net in base 3, but