Best Known (120−14, 120, s)-Nets in Base 3
(120−14, 120, 227762)-Net over F3 — Constructive and digital
Digital (106, 120, 227762)-net over F3, using
- 32 times duplication [i] based on digital (104, 118, 227762)-net over F3, using
- net defined by OOA [i] based on linear OOA(3118, 227762, F3, 14, 14) (dual of [(227762, 14), 3188550, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3118, 1594334, F3, 14) (dual of [1594334, 1594216, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3118, 1594336, F3, 14) (dual of [1594336, 1594218, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(3118, 1594323, F3, 14) (dual of [1594323, 1594205, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(3105, 1594323, F3, 13) (dual of [1594323, 1594218, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(30, 13, F3, 0) (dual of [13, 13, 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(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(3118, 1594336, F3, 14) (dual of [1594336, 1594218, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3118, 1594334, F3, 14) (dual of [1594334, 1594216, 15]-code), using
- net defined by OOA [i] based on linear OOA(3118, 227762, F3, 14, 14) (dual of [(227762, 14), 3188550, 15]-NRT-code), using
(120−14, 120, 531446)-Net over F3 — Digital
Digital (106, 120, 531446)-net over F3, using
- 31 times duplication [i] based on digital (105, 119, 531446)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3119, 531446, F3, 3, 14) (dual of [(531446, 3), 1594219, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3119, 1594338, F3, 14) (dual of [1594338, 1594219, 15]-code), using
- construction X4 applied to C([0,13]) ⊂ C([1,12]) [i] based on
- linear OA(3118, 1594322, F3, 14) (dual of [1594322, 1594204, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(3104, 1594322, F3, 12) (dual of [1594322, 1594218, 13]-code), using the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(315, 16, F3, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
- dual of repetition code with length 16 [i]
- linear OA(31, 16, F3, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X4 applied to C([0,13]) ⊂ C([1,12]) [i] based on
- OOA 3-folding [i] based on linear OA(3119, 1594338, F3, 14) (dual of [1594338, 1594219, 15]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3119, 531446, F3, 3, 14) (dual of [(531446, 3), 1594219, 15]-NRT-code), using
(120−14, 120, large)-Net in Base 3 — Upper bound on s
There is no (106, 120, large)-net in base 3, because
- 12 times m-reduction [i] would yield (106, 108, large)-net in base 3, but