Best Known (23, 23+8, s)-Nets in Base 3
(23, 23+8, 183)-Net over F3 — Constructive and digital
Digital (23, 31, 183)-net over F3, using
- net defined by OOA [i] based on linear OOA(331, 183, F3, 8, 8) (dual of [(183, 8), 1433, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(331, 732, F3, 8) (dual of [732, 701, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(331, 735, F3, 8) (dual of [735, 704, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(331, 729, F3, 8) (dual of [729, 698, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(325, 729, F3, 7) (dual of [729, 704, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(331, 735, F3, 8) (dual of [735, 704, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(331, 732, F3, 8) (dual of [732, 701, 9]-code), using
(23, 23+8, 367)-Net over F3 — Digital
Digital (23, 31, 367)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(331, 367, F3, 2, 8) (dual of [(367, 2), 703, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(331, 734, F3, 8) (dual of [734, 703, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(331, 735, F3, 8) (dual of [735, 704, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(331, 729, F3, 8) (dual of [729, 698, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(325, 729, F3, 7) (dual of [729, 704, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(331, 735, F3, 8) (dual of [735, 704, 9]-code), using
- OOA 2-folding [i] based on linear OA(331, 734, F3, 8) (dual of [734, 703, 9]-code), using
(23, 23+8, 5513)-Net in Base 3 — Upper bound on s
There is no (23, 31, 5514)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 617 842552 286633 > 331 [i]