Best Known (110−11, 110, s)-Nets in Base 3
(110−11, 110, 1677720)-Net over F3 — Constructive and digital
Digital (99, 110, 1677720)-net over F3, using
- 34 times duplication [i] based on digital (95, 106, 1677720)-net over F3, using
- net defined by OOA [i] based on linear OOA(3106, 1677720, F3, 11, 11) (dual of [(1677720, 11), 18454814, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3106, 8388601, F3, 11) (dual of [8388601, 8388495, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(3106, large, F3, 11) (dual of [large, large−106, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(3106, large, F3, 11) (dual of [large, large−106, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3106, 8388601, F3, 11) (dual of [8388601, 8388495, 12]-code), using
- net defined by OOA [i] based on linear OOA(3106, 1677720, F3, 11, 11) (dual of [(1677720, 11), 18454814, 12]-NRT-code), using
(110−11, 110, 4194303)-Net over F3 — Digital
Digital (99, 110, 4194303)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3110, 4194303, F3, 2, 11) (dual of [(4194303, 2), 8388496, 12]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(3106, 4194301, F3, 2, 11) (dual of [(4194301, 2), 8388496, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3106, 8388602, F3, 11) (dual of [8388602, 8388496, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(3106, large, F3, 11) (dual of [large, large−106, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(3106, large, F3, 11) (dual of [large, large−106, 12]-code), using
- OOA 2-folding [i] based on linear OA(3106, 8388602, F3, 11) (dual of [8388602, 8388496, 12]-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(3106, 4194301, F3, 2, 11) (dual of [(4194301, 2), 8388496, 12]-NRT-code), using
(110−11, 110, large)-Net in Base 3 — Upper bound on s
There is no (99, 110, large)-net in base 3, because
- 9 times m-reduction [i] would yield (99, 101, large)-net in base 3, but