Best Known (94, 94+11, s)-Nets in Base 3
(94, 94+11, 956603)-Net over F3 — Constructive and digital
Digital (94, 105, 956603)-net over F3, using
- net defined by OOA [i] based on linear OOA(3105, 956603, F3, 11, 11) (dual of [(956603, 11), 10522528, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3105, 4783016, F3, 11) (dual of [4783016, 4782911, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(3105, 4783017, F3, 11) (dual of [4783017, 4782912, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- linear OA(399, 4782969, F3, 11) (dual of [4782969, 4782870, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(357, 4782969, F3, 7) (dual of [4782969, 4782912, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- 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(10) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(3105, 4783017, F3, 11) (dual of [4783017, 4782912, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3105, 4783016, F3, 11) (dual of [4783016, 4782911, 12]-code), using
(94, 94+11, 2391508)-Net over F3 — Digital
Digital (94, 105, 2391508)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3105, 2391508, F3, 2, 11) (dual of [(2391508, 2), 4782911, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3105, 4783016, F3, 11) (dual of [4783016, 4782911, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(3105, 4783017, F3, 11) (dual of [4783017, 4782912, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- linear OA(399, 4782969, F3, 11) (dual of [4782969, 4782870, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(357, 4782969, F3, 7) (dual of [4782969, 4782912, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- 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(10) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(3105, 4783017, F3, 11) (dual of [4783017, 4782912, 12]-code), using
- OOA 2-folding [i] based on linear OA(3105, 4783016, F3, 11) (dual of [4783016, 4782911, 12]-code), using
(94, 94+11, large)-Net in Base 3 — Upper bound on s
There is no (94, 105, large)-net in base 3, because
- 9 times m-reduction [i] would yield (94, 96, large)-net in base 3, but