Best Known (89, 89+21, s)-Nets in Base 32
(89, 89+21, 838860)-Net over F32 — Constructive and digital
Digital (89, 110, 838860)-net over F32, using
- 329 times duplication [i] based on digital (80, 101, 838860)-net over F32, using
- net defined by OOA [i] based on linear OOA(32101, 838860, F32, 21, 21) (dual of [(838860, 21), 17615959, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(32101, 8388601, F32, 21) (dual of [8388601, 8388500, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(32101, large, F32, 21) (dual of [large, large−101, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(32101, large, F32, 21) (dual of [large, large−101, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(32101, 8388601, F32, 21) (dual of [8388601, 8388500, 22]-code), using
- net defined by OOA [i] based on linear OOA(32101, 838860, F32, 21, 21) (dual of [(838860, 21), 17615959, 22]-NRT-code), using
(89, 89+21, 838925)-Net in Base 32 — Constructive
(89, 110, 838925)-net in base 32, using
- (u, u+v)-construction [i] based on
- (2, 12, 65)-net in base 32, using
- base change [i] based on digital (0, 10, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- base change [i] based on digital (0, 10, 65)-net over F64, using
- (77, 98, 838860)-net in base 32, using
- net defined by OOA [i] based on OOA(3298, 838860, S32, 21, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(3298, 8388601, S32, 21), using
- discarding factors based on OA(3298, large, S32, 21), using
- discarding parts of the base [i] based on linear OA(6481, large, F64, 21) (dual of [large, large−81, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- discarding parts of the base [i] based on linear OA(6481, large, F64, 21) (dual of [large, large−81, 22]-code), using
- discarding factors based on OA(3298, large, S32, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(3298, 8388601, S32, 21), using
- net defined by OOA [i] based on OOA(3298, 838860, S32, 21, 21), using
- (2, 12, 65)-net in base 32, using
(89, 89+21, large)-Net over F32 — Digital
Digital (89, 110, large)-net over F32, using
- t-expansion [i] based on digital (87, 110, large)-net over F32, using
(89, 89+21, large)-Net in Base 32 — Upper bound on s
There is no (89, 110, large)-net in base 32, because
- 19 times m-reduction [i] would yield (89, 91, large)-net in base 32, but