Best Known (33, 48, s)-Nets in Base 16
(33, 48, 1032)-Net over F16 — Constructive and digital
Digital (33, 48, 1032)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (9, 16, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 8, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 8, 258)-net over F256, using
- digital (17, 32, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 16, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256 (see above)
- trace code for nets [i] based on digital (1, 16, 258)-net over F256, using
- digital (9, 16, 516)-net over F16, using
(33, 48, 5458)-Net over F16 — Digital
Digital (33, 48, 5458)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1648, 5458, F16, 15) (dual of [5458, 5410, 16]-code), using
- 1354 step Varšamov–Edel lengthening with (ri) = (2, 13 times 0, 1, 113 times 0, 1, 405 times 0, 1, 819 times 0) [i] based on linear OA(1643, 4099, F16, 15) (dual of [4099, 4056, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(1643, 4096, F16, 15) (dual of [4096, 4053, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(1640, 4096, F16, 14) (dual of [4096, 4056, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(160, 3, F16, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- 1354 step Varšamov–Edel lengthening with (ri) = (2, 13 times 0, 1, 113 times 0, 1, 405 times 0, 1, 819 times 0) [i] based on linear OA(1643, 4099, F16, 15) (dual of [4099, 4056, 16]-code), using
(33, 48, large)-Net in Base 16 — Upper bound on s
There is no (33, 48, large)-net in base 16, because
- 13 times m-reduction [i] would yield (33, 35, large)-net in base 16, but