Best Known (67, 104, s)-Nets in Base 32
(67, 104, 392)-Net over F32 — Constructive and digital
Digital (67, 104, 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, 25, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 44, 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
(67, 104, 910)-Net in Base 32 — Constructive
(67, 104, 910)-net in base 32, using
- 321 times duplication [i] based on (66, 103, 910)-net in base 32, using
- net defined by OOA [i] based on OOA(32103, 910, S32, 37, 37), using
- OOA 18-folding and stacking with additional row [i] based on OA(32103, 16381, S32, 37), using
- discarding factors based on OA(32103, 16386, S32, 37), using
- discarding parts of the base [i] based on linear OA(12873, 16386, F128, 37) (dual of [16386, 16313, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(35) [i] 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]
- linear OA(12871, 16384, F128, 36) (dual of [16384, 16313, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(36) ⊂ Ce(35) [i] based on
- discarding parts of the base [i] based on linear OA(12873, 16386, F128, 37) (dual of [16386, 16313, 38]-code), using
- discarding factors based on OA(32103, 16386, S32, 37), using
- OOA 18-folding and stacking with additional row [i] based on OA(32103, 16381, S32, 37), using
- net defined by OOA [i] based on OOA(32103, 910, S32, 37, 37), using
(67, 104, 10288)-Net over F32 — Digital
Digital (67, 104, 10288)-net over F32, using
(67, 104, large)-Net in Base 32 — Upper bound on s
There is no (67, 104, large)-net in base 32, because
- 35 times m-reduction [i] would yield (67, 69, large)-net in base 32, but