Best Known (240−24, 240, s)-Nets in Base 4
(240−24, 240, 699084)-Net over F4 — Constructive and digital
Digital (216, 240, 699084)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (12, 24, 34)-net over F4, using
- trace code for nets [i] based on digital (0, 12, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- trace code for nets [i] based on digital (0, 12, 17)-net over F16, 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 (12, 24, 34)-net over F4, using
(240−24, 240, large)-Net over F4 — Digital
Digital (216, 240, large)-net over F4, using
- 43 times duplication [i] based on digital (213, 237, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4237, large, F4, 24) (dual of [large, large−237, 25]-code), using
- 21 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]
- 21 times code embedding in larger space [i] based on linear OA(4216, large, F4, 24) (dual of [large, large−216, 25]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4237, large, F4, 24) (dual of [large, large−237, 25]-code), using
(240−24, 240, large)-Net in Base 4 — Upper bound on s
There is no (216, 240, large)-net in base 4, because
- 22 times m-reduction [i] would yield (216, 218, large)-net in base 4, but