Best Known (241−35, 241, s)-Nets in Base 3
(241−35, 241, 3475)-Net over F3 — Constructive and digital
Digital (206, 241, 3475)-net over F3, using
- 34 times duplication [i] based on digital (202, 237, 3475)-net over F3, using
- net defined by OOA [i] based on linear OOA(3237, 3475, F3, 35, 35) (dual of [(3475, 35), 121388, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(3237, 59076, F3, 35) (dual of [59076, 58839, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(3237, 59085, F3, 35) (dual of [59085, 58848, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- linear OA(3231, 59049, F3, 35) (dual of [59049, 58818, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3201, 59049, F3, 31) (dual of [59049, 58848, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(34) ⊂ Ce(30) [i] based on
- discarding factors / shortening the dual code based on linear OA(3237, 59085, F3, 35) (dual of [59085, 58848, 36]-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(3237, 59076, F3, 35) (dual of [59076, 58839, 36]-code), using
- net defined by OOA [i] based on linear OOA(3237, 3475, F3, 35, 35) (dual of [(3475, 35), 121388, 36]-NRT-code), using
(241−35, 241, 23376)-Net over F3 — Digital
Digital (206, 241, 23376)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3241, 23376, F3, 2, 35) (dual of [(23376, 2), 46511, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3241, 29544, F3, 2, 35) (dual of [(29544, 2), 58847, 36]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3240, 29544, F3, 2, 35) (dual of [(29544, 2), 58848, 36]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3238, 29543, F3, 2, 35) (dual of [(29543, 2), 58848, 36]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3238, 59086, F3, 35) (dual of [59086, 58848, 36]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3237, 59085, F3, 35) (dual of [59085, 58848, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- linear OA(3231, 59049, F3, 35) (dual of [59049, 58818, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3201, 59049, F3, 31) (dual of [59049, 58848, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(34) ⊂ Ce(30) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3237, 59085, F3, 35) (dual of [59085, 58848, 36]-code), using
- OOA 2-folding [i] based on linear OA(3238, 59086, F3, 35) (dual of [59086, 58848, 36]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3238, 29543, F3, 2, 35) (dual of [(29543, 2), 58848, 36]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3240, 29544, F3, 2, 35) (dual of [(29544, 2), 58848, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3241, 29544, F3, 2, 35) (dual of [(29544, 2), 58847, 36]-NRT-code), using
(241−35, 241, large)-Net in Base 3 — Upper bound on s
There is no (206, 241, large)-net in base 3, because
- 33 times m-reduction [i] would yield (206, 208, large)-net in base 3, but