Best Known (247−35, 247, s)-Nets in Base 3
(247−35, 247, 3477)-Net over F3 — Constructive and digital
Digital (212, 247, 3477)-net over F3, using
- 31 times duplication [i] based on digital (211, 246, 3477)-net over F3, using
- net defined by OOA [i] based on linear OOA(3246, 3477, F3, 35, 35) (dual of [(3477, 35), 121449, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(3246, 59110, F3, 35) (dual of [59110, 58864, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(3246, 59114, F3, 35) (dual of [59114, 58868, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(27) [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(3181, 59049, F3, 28) (dual of [59049, 58868, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(315, 65, F3, 6) (dual of [65, 50, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-code), using
- construction X applied to Ce(34) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(3246, 59114, F3, 35) (dual of [59114, 58868, 36]-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(3246, 59110, F3, 35) (dual of [59110, 58864, 36]-code), using
- net defined by OOA [i] based on linear OOA(3246, 3477, F3, 35, 35) (dual of [(3477, 35), 121449, 36]-NRT-code), using
(247−35, 247, 28730)-Net over F3 — Digital
Digital (212, 247, 28730)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3247, 28730, F3, 2, 35) (dual of [(28730, 2), 57213, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3247, 29557, F3, 2, 35) (dual of [(29557, 2), 58867, 36]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3246, 29557, F3, 2, 35) (dual of [(29557, 2), 58868, 36]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3246, 59114, F3, 35) (dual of [59114, 58868, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(27) [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(3181, 59049, F3, 28) (dual of [59049, 58868, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(315, 65, F3, 6) (dual of [65, 50, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-code), using
- construction X applied to Ce(34) ⊂ Ce(27) [i] based on
- OOA 2-folding [i] based on linear OA(3246, 59114, F3, 35) (dual of [59114, 58868, 36]-code), using
- 31 times duplication [i] based on linear OOA(3246, 29557, F3, 2, 35) (dual of [(29557, 2), 58868, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3247, 29557, F3, 2, 35) (dual of [(29557, 2), 58867, 36]-NRT-code), using
(247−35, 247, large)-Net in Base 3 — Upper bound on s
There is no (212, 247, large)-net in base 3, because
- 33 times m-reduction [i] would yield (212, 214, large)-net in base 3, but