Best Known (225−24, 225, s)-Nets in Base 3
(225−24, 225, 398581)-Net over F3 — Constructive and digital
Digital (201, 225, 398581)-net over F3, using
- net defined by OOA [i] based on linear OOA(3225, 398581, F3, 24, 24) (dual of [(398581, 24), 9565719, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3225, 4782972, F3, 24) (dual of [4782972, 4782747, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3225, 4782983, F3, 24) (dual of [4782983, 4782758, 25]-code), using
- 1 times truncation [i] based on linear OA(3226, 4782984, F3, 25) (dual of [4782984, 4782758, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(3225, 4782969, F3, 25) (dual of [4782969, 4782744, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3211, 4782969, F3, 23) (dual of [4782969, 4782758, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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 X applied to Ce(24) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(3226, 4782984, F3, 25) (dual of [4782984, 4782758, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3225, 4782983, F3, 24) (dual of [4782983, 4782758, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(3225, 4782972, F3, 24) (dual of [4782972, 4782747, 25]-code), using
(225−24, 225, 1195745)-Net over F3 — Digital
Digital (201, 225, 1195745)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3225, 1195745, F3, 4, 24) (dual of [(1195745, 4), 4782755, 25]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3225, 4782980, F3, 24) (dual of [4782980, 4782755, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3225, 4782983, F3, 24) (dual of [4782983, 4782758, 25]-code), using
- 1 times truncation [i] based on linear OA(3226, 4782984, F3, 25) (dual of [4782984, 4782758, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(3225, 4782969, F3, 25) (dual of [4782969, 4782744, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3211, 4782969, F3, 23) (dual of [4782969, 4782758, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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 X applied to Ce(24) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(3226, 4782984, F3, 25) (dual of [4782984, 4782758, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3225, 4782983, F3, 24) (dual of [4782983, 4782758, 25]-code), using
- OOA 4-folding [i] based on linear OA(3225, 4782980, F3, 24) (dual of [4782980, 4782755, 25]-code), using
(225−24, 225, large)-Net in Base 3 — Upper bound on s
There is no (201, 225, large)-net in base 3, because
- 22 times m-reduction [i] would yield (201, 203, large)-net in base 3, but