Best Known (145−24, 145, s)-Nets in Base 3
(145−24, 145, 1641)-Net over F3 — Constructive and digital
Digital (121, 145, 1641)-net over F3, using
- net defined by OOA [i] based on linear OOA(3145, 1641, F3, 24, 24) (dual of [(1641, 24), 39239, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3145, 19692, F3, 24) (dual of [19692, 19547, 25]-code), using
- 1 times truncation [i] based on linear OA(3146, 19693, F3, 25) (dual of [19693, 19547, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(3145, 19683, F3, 25) (dual of [19683, 19538, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3136, 19683, F3, 23) (dual of [19683, 19547, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(31, 10, F3, 1) (dual of [10, 9, 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(3146, 19693, F3, 25) (dual of [19693, 19547, 26]-code), using
- OA 12-folding and stacking [i] based on linear OA(3145, 19692, F3, 24) (dual of [19692, 19547, 25]-code), using
(145−24, 145, 7679)-Net over F3 — Digital
Digital (121, 145, 7679)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3145, 7679, F3, 2, 24) (dual of [(7679, 2), 15213, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3145, 9846, F3, 2, 24) (dual of [(9846, 2), 19547, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3145, 19692, F3, 24) (dual of [19692, 19547, 25]-code), using
- 1 times truncation [i] based on linear OA(3146, 19693, F3, 25) (dual of [19693, 19547, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(3145, 19683, F3, 25) (dual of [19683, 19538, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3136, 19683, F3, 23) (dual of [19683, 19547, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(31, 10, F3, 1) (dual of [10, 9, 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(3146, 19693, F3, 25) (dual of [19693, 19547, 26]-code), using
- OOA 2-folding [i] based on linear OA(3145, 19692, F3, 24) (dual of [19692, 19547, 25]-code), using
- discarding factors / shortening the dual code based on linear OOA(3145, 9846, F3, 2, 24) (dual of [(9846, 2), 19547, 25]-NRT-code), using
(145−24, 145, 1540080)-Net in Base 3 — Upper bound on s
There is no (121, 145, 1540081)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1522 595895 913913 773885 215969 505857 381227 164686 407300 706373 090187 389809 > 3145 [i]