Best Known (108, 128, s)-Nets in Base 16
(108, 128, 1677753)-Net over F16 — Constructive and digital
Digital (108, 128, 1677753)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (2, 12, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- digital (96, 116, 1677720)-net over F16, using
- net defined by OOA [i] based on linear OOA(16116, 1677720, F16, 22, 20) (dual of [(1677720, 22), 36909724, 21]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(16116, 8388601, F16, 2, 20) (dual of [(8388601, 2), 16777086, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(16116, 8388602, F16, 2, 20) (dual of [(8388602, 2), 16777088, 21]-NRT-code), using
- trace code [i] based on linear OOA(25658, 4194301, F256, 2, 20) (dual of [(4194301, 2), 8388544, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25658, 8388602, F256, 20) (dual of [8388602, 8388544, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(25658, large, F256, 20) (dual of [large, large−58, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(25658, large, F256, 20) (dual of [large, large−58, 21]-code), using
- OOA 2-folding [i] based on linear OA(25658, 8388602, F256, 20) (dual of [8388602, 8388544, 21]-code), using
- trace code [i] based on linear OOA(25658, 4194301, F256, 2, 20) (dual of [(4194301, 2), 8388544, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(16116, 8388602, F16, 2, 20) (dual of [(8388602, 2), 16777088, 21]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(16116, 8388601, F16, 2, 20) (dual of [(8388601, 2), 16777086, 21]-NRT-code), using
- net defined by OOA [i] based on linear OOA(16116, 1677720, F16, 22, 20) (dual of [(1677720, 22), 36909724, 21]-NRT-code), using
- digital (2, 12, 33)-net over F16, using
(108, 128, large)-Net over F16 — Digital
Digital (108, 128, large)-net over F16, using
- 161 times duplication [i] based on digital (107, 127, large)-net over F16, using
- t-expansion [i] based on digital (104, 127, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16127, large, F16, 23) (dual of [large, large−127, 24]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16127, large, F16, 23) (dual of [large, large−127, 24]-code), using
- t-expansion [i] based on digital (104, 127, large)-net over F16, using
(108, 128, large)-Net in Base 16 — Upper bound on s
There is no (108, 128, large)-net in base 16, because
- 18 times m-reduction [i] would yield (108, 110, large)-net in base 16, but