Best Known (97−21, 97, s)-Nets in Base 7
(97−21, 97, 1683)-Net over F7 — Constructive and digital
Digital (76, 97, 1683)-net over F7, using
- 72 times duplication [i] based on digital (74, 95, 1683)-net over F7, using
- net defined by OOA [i] based on linear OOA(795, 1683, F7, 21, 21) (dual of [(1683, 21), 35248, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(795, 16831, F7, 21) (dual of [16831, 16736, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(795, 16832, F7, 21) (dual of [16832, 16737, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(791, 16808, F7, 21) (dual of [16808, 16717, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(771, 16808, F7, 17) (dual of [16808, 16737, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(74, 24, F7, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,7)), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(795, 16832, F7, 21) (dual of [16832, 16737, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(795, 16831, F7, 21) (dual of [16831, 16736, 22]-code), using
- net defined by OOA [i] based on linear OOA(795, 1683, F7, 21, 21) (dual of [(1683, 21), 35248, 22]-NRT-code), using
(97−21, 97, 17383)-Net over F7 — Digital
Digital (76, 97, 17383)-net over F7, using
(97−21, 97, large)-Net in Base 7 — Upper bound on s
There is no (76, 97, large)-net in base 7, because
- 19 times m-reduction [i] would yield (76, 78, large)-net in base 7, but