Best Known (232−28, 232, s)-Nets in Base 3
(232−28, 232, 37967)-Net over F3 — Constructive and digital
Digital (204, 232, 37967)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 15, 7)-net over F3, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- digital (189, 217, 37960)-net over F3, using
- net defined by OOA [i] based on linear OOA(3217, 37960, F3, 28, 28) (dual of [(37960, 28), 1062663, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(3217, 531440, F3, 28) (dual of [531440, 531223, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3217, 531441, F3, 28) (dual of [531441, 531224, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(3217, 531441, F3, 28) (dual of [531441, 531224, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(3217, 531440, F3, 28) (dual of [531440, 531223, 29]-code), using
- net defined by OOA [i] based on linear OOA(3217, 37960, F3, 28, 28) (dual of [(37960, 28), 1062663, 29]-NRT-code), using
- digital (1, 15, 7)-net over F3, using
(232−28, 232, 174907)-Net over F3 — Digital
Digital (204, 232, 174907)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3232, 174907, F3, 3, 28) (dual of [(174907, 3), 524489, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3232, 177168, F3, 3, 28) (dual of [(177168, 3), 531272, 29]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3229, 177167, F3, 3, 28) (dual of [(177167, 3), 531272, 29]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3229, 531501, F3, 28) (dual of [531501, 531272, 29]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3228, 531500, F3, 28) (dual of [531500, 531272, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(3217, 531441, F3, 28) (dual of [531441, 531224, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(311, 59, F3, 5) (dual of [59, 48, 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 Ce(27) ⊂ Ce(21) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3228, 531500, F3, 28) (dual of [531500, 531272, 29]-code), using
- OOA 3-folding [i] based on linear OA(3229, 531501, F3, 28) (dual of [531501, 531272, 29]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3229, 177167, F3, 3, 28) (dual of [(177167, 3), 531272, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3232, 177168, F3, 3, 28) (dual of [(177168, 3), 531272, 29]-NRT-code), using
(232−28, 232, large)-Net in Base 3 — Upper bound on s
There is no (204, 232, large)-net in base 3, because
- 26 times m-reduction [i] would yield (204, 206, large)-net in base 3, but