Best Known (68, 105, s)-Nets in Base 32
(68, 105, 392)-Net over F32 — Constructive and digital
Digital (68, 105, 392)-net over F32, using
- 1 times m-reduction [i] based on digital (68, 106, 392)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (7, 16, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (7, 19, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 26, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 45, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 16, 98)-net over F32, using
- generalized (u, u+v)-construction [i] based on
(68, 105, 910)-Net in Base 32 — Constructive
(68, 105, 910)-net in base 32, using
- base change [i] based on digital (38, 75, 910)-net over F128, using
- 1282 times duplication [i] based on digital (36, 73, 910)-net over F128, using
- net defined by OOA [i] based on linear OOA(12873, 910, F128, 37, 37) (dual of [(910, 37), 33597, 38]-NRT-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(12873, 16381, F128, 37) (dual of [16381, 16308, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(12873, 16384, F128, 37) (dual of [16384, 16311, 38]-code), using
- an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- discarding factors / shortening the dual code based on linear OA(12873, 16384, F128, 37) (dual of [16384, 16311, 38]-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(12873, 16381, F128, 37) (dual of [16381, 16308, 38]-code), using
- net defined by OOA [i] based on linear OOA(12873, 910, F128, 37, 37) (dual of [(910, 37), 33597, 38]-NRT-code), using
- 1282 times duplication [i] based on digital (36, 73, 910)-net over F128, using
(68, 105, 11326)-Net over F32 — Digital
Digital (68, 105, 11326)-net over F32, using
(68, 105, large)-Net in Base 32 — Upper bound on s
There is no (68, 105, large)-net in base 32, because
- 35 times m-reduction [i] would yield (68, 70, large)-net in base 32, but