Best Known (204, 204+24, s)-Nets in Base 4
(204, 204+24, 699055)-Net over F4 — Constructive and digital
Digital (204, 228, 699055)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 12, 5)-net over F4, using
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 0 and N(F) ≥ 5, using
- the rational function field F4(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- digital (192, 216, 699050)-net over F4, using
- net defined by OOA [i] based on linear OOA(4216, 699050, F4, 24, 24) (dual of [(699050, 24), 16776984, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(4216, 8388600, F4, 24) (dual of [8388600, 8388384, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4216, large, F4, 24) (dual of [large, large−216, 25]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(4216, large, F4, 24) (dual of [large, large−216, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(4216, 8388600, F4, 24) (dual of [8388600, 8388384, 25]-code), using
- net defined by OOA [i] based on linear OOA(4216, 699050, F4, 24, 24) (dual of [(699050, 24), 16776984, 25]-NRT-code), using
- digital (0, 12, 5)-net over F4, using
(204, 204+24, 4919202)-Net over F4 — Digital
Digital (204, 228, 4919202)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4228, 4919202, F4, 24) (dual of [4919202, 4918974, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4228, large, F4, 24) (dual of [large, large−228, 25]-code), using
- 12 times code embedding in larger space [i] based on linear OA(4216, large, F4, 24) (dual of [large, large−216, 25]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- 12 times code embedding in larger space [i] based on linear OA(4216, large, F4, 24) (dual of [large, large−216, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4228, large, F4, 24) (dual of [large, large−228, 25]-code), using
(204, 204+24, large)-Net in Base 4 — Upper bound on s
There is no (204, 228, large)-net in base 4, because
- 22 times m-reduction [i] would yield (204, 206, large)-net in base 4, but