Best Known (102, 119, s)-Nets in Base 3
(102, 119, 7386)-Net over F3 — Constructive and digital
Digital (102, 119, 7386)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 4)-net over F3, using
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 0 and N(F) ≥ 4, using
- the rational function field F3(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- digital (94, 111, 7382)-net over F3, using
- net defined by OOA [i] based on linear OOA(3111, 7382, F3, 17, 17) (dual of [(7382, 17), 125383, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3111, 59057, F3, 17) (dual of [59057, 58946, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3111, 59059, F3, 17) (dual of [59059, 58948, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [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(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(30, 10, F3, 0) (dual of [10, 10, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(3111, 59059, F3, 17) (dual of [59059, 58948, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3111, 59057, F3, 17) (dual of [59057, 58946, 18]-code), using
- net defined by OOA [i] based on linear OOA(3111, 7382, F3, 17, 17) (dual of [(7382, 17), 125383, 18]-NRT-code), using
- digital (0, 8, 4)-net over F3, using
(102, 119, 29350)-Net over F3 — Digital
Digital (102, 119, 29350)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3119, 29350, F3, 2, 17) (dual of [(29350, 2), 58581, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3119, 29543, F3, 2, 17) (dual of [(29543, 2), 58967, 18]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3118, 29543, F3, 2, 17) (dual of [(29543, 2), 58968, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3118, 59086, F3, 17) (dual of [59086, 58968, 18]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3117, 59085, F3, 17) (dual of [59085, 58968, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [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(381, 59049, F3, 13) (dual of [59049, 58968, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(16) ⊂ Ce(12) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3117, 59085, F3, 17) (dual of [59085, 58968, 18]-code), using
- OOA 2-folding [i] based on linear OA(3118, 59086, F3, 17) (dual of [59086, 58968, 18]-code), using
- 31 times duplication [i] based on linear OOA(3118, 29543, F3, 2, 17) (dual of [(29543, 2), 58968, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3119, 29543, F3, 2, 17) (dual of [(29543, 2), 58967, 18]-NRT-code), using
(102, 119, large)-Net in Base 3 — Upper bound on s
There is no (102, 119, large)-net in base 3, because
- 15 times m-reduction [i] would yield (102, 104, large)-net in base 3, but