Best Known (83, 94, s)-Nets in Base 3
(83, 94, 318867)-Net over F3 — Constructive and digital
Digital (83, 94, 318867)-net over F3, using
- 32 times duplication [i] based on digital (81, 92, 318867)-net over F3, using
- net defined by OOA [i] based on linear OOA(392, 318867, F3, 11, 11) (dual of [(318867, 11), 3507445, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(392, 1594336, F3, 11) (dual of [1594336, 1594244, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(392, 1594323, F3, 11) (dual of [1594323, 1594231, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(379, 1594323, F3, 10) (dual of [1594323, 1594244, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(10) ⊂ Ce(9) [i] based on
- OOA 5-folding and stacking with additional row [i] based on linear OA(392, 1594336, F3, 11) (dual of [1594336, 1594244, 12]-code), using
- net defined by OOA [i] based on linear OOA(392, 318867, F3, 11, 11) (dual of [(318867, 11), 3507445, 12]-NRT-code), using
(83, 94, 577496)-Net over F3 — Digital
Digital (83, 94, 577496)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(394, 577496, F3, 2, 11) (dual of [(577496, 2), 1154898, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(394, 797169, F3, 2, 11) (dual of [(797169, 2), 1594244, 12]-NRT-code), using
- 31 times duplication [i] based on linear OOA(393, 797169, F3, 2, 11) (dual of [(797169, 2), 1594245, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(393, 1594338, F3, 11) (dual of [1594338, 1594245, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(392, 1594323, F3, 11) (dual of [1594323, 1594231, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(379, 1594323, F3, 10) (dual of [1594323, 1594244, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(314, 15, F3, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,3)), using
- dual of repetition code with length 15 [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 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 Ce(10) ⊂ Ce(9) [i] based on
- OOA 2-folding [i] based on linear OA(393, 1594338, F3, 11) (dual of [1594338, 1594245, 12]-code), using
- 31 times duplication [i] based on linear OOA(393, 797169, F3, 2, 11) (dual of [(797169, 2), 1594245, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(394, 797169, F3, 2, 11) (dual of [(797169, 2), 1594244, 12]-NRT-code), using
(83, 94, large)-Net in Base 3 — Upper bound on s
There is no (83, 94, large)-net in base 3, because
- 9 times m-reduction [i] would yield (83, 85, large)-net in base 3, but