Best Known (83, 83+14, s)-Nets in Base 3
(83, 83+14, 8440)-Net over F3 — Constructive and digital
Digital (83, 97, 8440)-net over F3, using
- net defined by OOA [i] based on linear OOA(397, 8440, F3, 14, 14) (dual of [(8440, 14), 118063, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(397, 59080, F3, 14) (dual of [59080, 58983, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(397, 59085, F3, 14) (dual of [59085, 58988, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- 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(361, 59049, F3, 10) (dual of [59049, 58988, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(13) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(397, 59085, F3, 14) (dual of [59085, 58988, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(397, 59080, F3, 14) (dual of [59080, 58983, 15]-code), using
(83, 83+14, 29542)-Net over F3 — Digital
Digital (83, 97, 29542)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(397, 29542, F3, 2, 14) (dual of [(29542, 2), 58987, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(397, 59084, F3, 14) (dual of [59084, 58987, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(397, 59085, F3, 14) (dual of [59085, 58988, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- 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(361, 59049, F3, 10) (dual of [59049, 58988, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(13) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(397, 59085, F3, 14) (dual of [59085, 58988, 15]-code), using
- OOA 2-folding [i] based on linear OA(397, 59084, F3, 14) (dual of [59084, 58987, 15]-code), using
(83, 83+14, 6909166)-Net in Base 3 — Upper bound on s
There is no (83, 97, 6909167)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 19088 074597 215476 371085 284768 106490 580839 639219 > 397 [i]