Best Known (212, 236, s)-Nets in Base 3
(212, 236, 398586)-Net over F3 — Constructive and digital
Digital (212, 236, 398586)-net over F3, using
- t-expansion [i] based on digital (211, 236, 398586)-net over F3, using
- net defined by OOA [i] based on linear OOA(3236, 398586, F3, 25, 25) (dual of [(398586, 25), 9964414, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3236, 4783033, F3, 25) (dual of [4783033, 4782797, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 4783037, F3, 25) (dual of [4783037, 4782801, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(3225, 4782970, F3, 25) (dual of [4782970, 4782745, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3169, 4782970, F3, 19) (dual of [4782970, 4782801, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(311, 67, F3, 5) (dual of [67, 56, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3236, 4783037, F3, 25) (dual of [4783037, 4782801, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3236, 4783033, F3, 25) (dual of [4783033, 4782797, 26]-code), using
- net defined by OOA [i] based on linear OOA(3236, 398586, F3, 25, 25) (dual of [(398586, 25), 9964414, 26]-NRT-code), using
(212, 236, 1502219)-Net over F3 — Digital
Digital (212, 236, 1502219)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3236, 1502219, F3, 3, 24) (dual of [(1502219, 3), 4506421, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3236, 1594345, F3, 3, 24) (dual of [(1594345, 3), 4782799, 25]-NRT-code), using
- strength reduction [i] based on linear OOA(3236, 1594345, F3, 3, 25) (dual of [(1594345, 3), 4782799, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3236, 4783035, F3, 25) (dual of [4783035, 4782799, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 4783037, F3, 25) (dual of [4783037, 4782801, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(3225, 4782970, F3, 25) (dual of [4782970, 4782745, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3169, 4782970, F3, 19) (dual of [4782970, 4782801, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(311, 67, F3, 5) (dual of [67, 56, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3236, 4783037, F3, 25) (dual of [4783037, 4782801, 26]-code), using
- OOA 3-folding [i] based on linear OA(3236, 4783035, F3, 25) (dual of [4783035, 4782799, 26]-code), using
- strength reduction [i] based on linear OOA(3236, 1594345, F3, 3, 25) (dual of [(1594345, 3), 4782799, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3236, 1594345, F3, 3, 24) (dual of [(1594345, 3), 4782799, 25]-NRT-code), using
(212, 236, large)-Net in Base 3 — Upper bound on s
There is no (212, 236, large)-net in base 3, because
- 22 times m-reduction [i] would yield (212, 214, large)-net in base 3, but