Best Known (107−15, 107, s)-Nets in Base 3
(107−15, 107, 8440)-Net over F3 — Constructive and digital
Digital (92, 107, 8440)-net over F3, using
- net defined by OOA [i] based on linear OOA(3107, 8440, F3, 15, 15) (dual of [(8440, 15), 126493, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3107, 59081, F3, 15) (dual of [59081, 58974, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3107, 59085, F3, 15) (dual of [59085, 58978, 16]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(3101, 59049, F3, 16) (dual of [59049, 58948, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(371, 59049, F3, 11) (dual of [59049, 58978, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(15) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(3107, 59085, F3, 15) (dual of [59085, 58978, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3107, 59081, F3, 15) (dual of [59081, 58974, 16]-code), using
(107−15, 107, 29542)-Net over F3 — Digital
Digital (92, 107, 29542)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3107, 29542, F3, 2, 15) (dual of [(29542, 2), 58977, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3107, 59084, F3, 15) (dual of [59084, 58977, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3107, 59085, F3, 15) (dual of [59085, 58978, 16]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(3101, 59049, F3, 16) (dual of [59049, 58948, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(371, 59049, F3, 11) (dual of [59049, 58978, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(15) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(3107, 59085, F3, 15) (dual of [59085, 58978, 16]-code), using
- OOA 2-folding [i] based on linear OA(3107, 59084, F3, 15) (dual of [59084, 58977, 16]-code), using
(107−15, 107, large)-Net in Base 3 — Upper bound on s
There is no (92, 107, large)-net in base 3, because
- 13 times m-reduction [i] would yield (92, 94, large)-net in base 3, but