Best Known (73, 73+17, s)-Nets in Base 7
(73, 73+17, 14709)-Net over F7 — Constructive and digital
Digital (73, 90, 14709)-net over F7, using
- net defined by OOA [i] based on linear OOA(790, 14709, F7, 17, 17) (dual of [(14709, 17), 249963, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(790, 117673, F7, 17) (dual of [117673, 117583, 18]-code), using
- construction XX applied to Ce(16) ⊂ Ce(12) ⊂ Ce(11) [i] based on
- linear OA(785, 117649, F7, 17) (dual of [117649, 117564, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(767, 117649, F7, 13) (dual of [117649, 117582, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(761, 117649, F7, 12) (dual of [117649, 117588, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(74, 23, F7, 3) (dual of [23, 19, 4]-code or 23-cap in PG(3,7)), using
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(16) ⊂ Ce(12) ⊂ Ce(11) [i] based on
- OOA 8-folding and stacking with additional row [i] based on linear OA(790, 117673, F7, 17) (dual of [117673, 117583, 18]-code), using
(73, 73+17, 110619)-Net over F7 — Digital
Digital (73, 90, 110619)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(790, 110619, F7, 17) (dual of [110619, 110529, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(790, 117673, F7, 17) (dual of [117673, 117583, 18]-code), using
- construction XX applied to Ce(16) ⊂ Ce(12) ⊂ Ce(11) [i] based on
- linear OA(785, 117649, F7, 17) (dual of [117649, 117564, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(767, 117649, F7, 13) (dual of [117649, 117582, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(761, 117649, F7, 12) (dual of [117649, 117588, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(74, 23, F7, 3) (dual of [23, 19, 4]-code or 23-cap in PG(3,7)), using
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(16) ⊂ Ce(12) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(790, 117673, F7, 17) (dual of [117673, 117583, 18]-code), using
(73, 73+17, large)-Net in Base 7 — Upper bound on s
There is no (73, 90, large)-net in base 7, because
- 15 times m-reduction [i] would yield (73, 75, large)-net in base 7, but