Best Known (94−21, 94, s)-Nets in Base 7
(94−21, 94, 1682)-Net over F7 — Constructive and digital
Digital (73, 94, 1682)-net over F7, using
- net defined by OOA [i] based on linear OOA(794, 1682, F7, 21, 21) (dual of [(1682, 21), 35228, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(794, 16821, F7, 21) (dual of [16821, 16727, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(794, 16825, F7, 21) (dual of [16825, 16731, 22]-code), using
- 1 times truncation [i] based on linear OA(795, 16826, F7, 22) (dual of [16826, 16731, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- linear OA(791, 16807, F7, 22) (dual of [16807, 16716, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(776, 16807, F7, 18) (dual of [16807, 16731, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(74, 19, F7, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,7)), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- 1 times truncation [i] based on linear OA(795, 16826, F7, 22) (dual of [16826, 16731, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(794, 16825, F7, 21) (dual of [16825, 16731, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(794, 16821, F7, 21) (dual of [16821, 16727, 22]-code), using
(94−21, 94, 16825)-Net over F7 — Digital
Digital (73, 94, 16825)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(794, 16825, F7, 21) (dual of [16825, 16731, 22]-code), using
- 1 times truncation [i] based on linear OA(795, 16826, F7, 22) (dual of [16826, 16731, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- linear OA(791, 16807, F7, 22) (dual of [16807, 16716, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(776, 16807, F7, 18) (dual of [16807, 16731, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(74, 19, F7, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,7)), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- 1 times truncation [i] based on linear OA(795, 16826, F7, 22) (dual of [16826, 16731, 23]-code), using
(94−21, 94, large)-Net in Base 7 — Upper bound on s
There is no (73, 94, large)-net in base 7, because
- 19 times m-reduction [i] would yield (73, 75, large)-net in base 7, but