Best Known (183−24, 183, s)-Nets in Base 3
(183−24, 183, 14765)-Net over F3 — Constructive and digital
Digital (159, 183, 14765)-net over F3, using
- net defined by OOA [i] based on linear OOA(3183, 14765, F3, 24, 24) (dual of [(14765, 24), 354177, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3183, 177180, F3, 24) (dual of [177180, 176997, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3183, 177186, F3, 24) (dual of [177186, 177003, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(3177, 177147, F3, 25) (dual of [177147, 176970, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3144, 177147, F3, 20) (dual of [177147, 177003, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(36, 39, F3, 3) (dual of [39, 33, 4]-code or 39-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3183, 177186, F3, 24) (dual of [177186, 177003, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(3183, 177180, F3, 24) (dual of [177180, 176997, 25]-code), using
(183−24, 183, 59062)-Net over F3 — Digital
Digital (159, 183, 59062)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3183, 59062, F3, 3, 24) (dual of [(59062, 3), 177003, 25]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3183, 177186, F3, 24) (dual of [177186, 177003, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(3177, 177147, F3, 25) (dual of [177147, 176970, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3144, 177147, F3, 20) (dual of [177147, 177003, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(36, 39, F3, 3) (dual of [39, 33, 4]-code or 39-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- OOA 3-folding [i] based on linear OA(3183, 177186, F3, 24) (dual of [177186, 177003, 25]-code), using
(183−24, 183, large)-Net in Base 3 — Upper bound on s
There is no (159, 183, large)-net in base 3, because
- 22 times m-reduction [i] would yield (159, 161, large)-net in base 3, but