Best Known (36, 47, s)-Nets in Base 7
(36, 47, 3363)-Net over F7 — Constructive and digital
Digital (36, 47, 3363)-net over F7, using
- net defined by OOA [i] based on linear OOA(747, 3363, F7, 11, 11) (dual of [(3363, 11), 36946, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(747, 16816, F7, 11) (dual of [16816, 16769, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(747, 16818, F7, 11) (dual of [16818, 16771, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(746, 16807, F7, 11) (dual of [16807, 16761, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(736, 16807, F7, 9) (dual of [16807, 16771, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(71, 11, F7, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(747, 16818, F7, 11) (dual of [16818, 16771, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(747, 16816, F7, 11) (dual of [16816, 16769, 12]-code), using
(36, 47, 14416)-Net over F7 — Digital
Digital (36, 47, 14416)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(747, 14416, F7, 11) (dual of [14416, 14369, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(747, 16818, F7, 11) (dual of [16818, 16771, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(746, 16807, F7, 11) (dual of [16807, 16761, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(736, 16807, F7, 9) (dual of [16807, 16771, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(71, 11, F7, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(747, 16818, F7, 11) (dual of [16818, 16771, 12]-code), using
(36, 47, large)-Net in Base 7 — Upper bound on s
There is no (36, 47, large)-net in base 7, because
- 9 times m-reduction [i] would yield (36, 38, large)-net in base 7, but