Best Known (115−17, 115, s)-Nets in Base 3
(115−17, 115, 7384)-Net over F3 — Constructive and digital
Digital (98, 115, 7384)-net over F3, using
- net defined by OOA [i] based on linear OOA(3115, 7384, F3, 17, 17) (dual of [(7384, 17), 125413, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3115, 59073, F3, 17) (dual of [59073, 58958, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(3111, 59049, F3, 17) (dual of [59049, 58938, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(391, 59049, F3, 14) (dual of [59049, 58958, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(34, 24, F3, 2) (dual of [24, 20, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- OOA 8-folding and stacking with additional row [i] based on linear OA(3115, 59073, F3, 17) (dual of [59073, 58958, 18]-code), using
(115−17, 115, 21440)-Net over F3 — Digital
Digital (98, 115, 21440)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3115, 21440, F3, 2, 17) (dual of [(21440, 2), 42765, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3115, 29536, F3, 2, 17) (dual of [(29536, 2), 58957, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3115, 59072, F3, 17) (dual of [59072, 58957, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3115, 59073, F3, 17) (dual of [59073, 58958, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(3111, 59049, F3, 17) (dual of [59049, 58938, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(391, 59049, F3, 14) (dual of [59049, 58958, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(34, 24, F3, 2) (dual of [24, 20, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(3115, 59073, F3, 17) (dual of [59073, 58958, 18]-code), using
- OOA 2-folding [i] based on linear OA(3115, 59072, F3, 17) (dual of [59072, 58957, 18]-code), using
- discarding factors / shortening the dual code based on linear OOA(3115, 29536, F3, 2, 17) (dual of [(29536, 2), 58957, 18]-NRT-code), using
(115−17, 115, large)-Net in Base 3 — Upper bound on s
There is no (98, 115, large)-net in base 3, because
- 15 times m-reduction [i] would yield (98, 100, large)-net in base 3, but