Best Known (153, 153+26, s)-Nets in Base 3
(153, 153+26, 4545)-Net over F3 — Constructive and digital
Digital (153, 179, 4545)-net over F3, using
- 32 times duplication [i] based on digital (151, 177, 4545)-net over F3, using
- net defined by OOA [i] based on linear OOA(3177, 4545, F3, 26, 26) (dual of [(4545, 26), 117993, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3177, 59085, F3, 26) (dual of [59085, 58908, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- 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(3141, 59049, F3, 22) (dual of [59049, 58908, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(36, 36, F3, 3) (dual of [36, 30, 4]-code or 36-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(25) ⊂ Ce(21) [i] based on
- OA 13-folding and stacking [i] based on linear OA(3177, 59085, F3, 26) (dual of [59085, 58908, 27]-code), using
- net defined by OOA [i] based on linear OOA(3177, 4545, F3, 26, 26) (dual of [(4545, 26), 117993, 27]-NRT-code), using
(153, 153+26, 22118)-Net over F3 — Digital
Digital (153, 179, 22118)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3179, 22118, F3, 2, 26) (dual of [(22118, 2), 44057, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3179, 29543, F3, 2, 26) (dual of [(29543, 2), 58907, 27]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3178, 29543, F3, 2, 26) (dual of [(29543, 2), 58908, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3178, 59086, F3, 26) (dual of [59086, 58908, 27]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3177, 59085, F3, 26) (dual of [59085, 58908, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- 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(3141, 59049, F3, 22) (dual of [59049, 58908, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(36, 36, F3, 3) (dual of [36, 30, 4]-code or 36-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(25) ⊂ Ce(21) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3177, 59085, F3, 26) (dual of [59085, 58908, 27]-code), using
- OOA 2-folding [i] based on linear OA(3178, 59086, F3, 26) (dual of [59086, 58908, 27]-code), using
- 31 times duplication [i] based on linear OOA(3178, 29543, F3, 2, 26) (dual of [(29543, 2), 58908, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3179, 29543, F3, 2, 26) (dual of [(29543, 2), 58907, 27]-NRT-code), using
(153, 153+26, large)-Net in Base 3 — Upper bound on s
There is no (153, 179, large)-net in base 3, because
- 24 times m-reduction [i] would yield (153, 155, large)-net in base 3, but