Best Known (50, 64, s)-Nets in Base 7
(50, 64, 2403)-Net over F7 — Constructive and digital
Digital (50, 64, 2403)-net over F7, using
- net defined by OOA [i] based on linear OOA(764, 2403, F7, 14, 14) (dual of [(2403, 14), 33578, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(764, 16821, F7, 14) (dual of [16821, 16757, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(764, 16825, F7, 14) (dual of [16825, 16761, 15]-code), using
- 1 times truncation [i] based on linear OA(765, 16826, F7, 15) (dual of [16826, 16761, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- linear OA(761, 16807, F7, 15) (dual of [16807, 16746, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 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(74, 19, F7, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,7)), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- 1 times truncation [i] based on linear OA(765, 16826, F7, 15) (dual of [16826, 16761, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(764, 16825, F7, 14) (dual of [16825, 16761, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(764, 16821, F7, 14) (dual of [16821, 16757, 15]-code), using
(50, 64, 16825)-Net over F7 — Digital
Digital (50, 64, 16825)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(764, 16825, F7, 14) (dual of [16825, 16761, 15]-code), using
- 1 times truncation [i] based on linear OA(765, 16826, F7, 15) (dual of [16826, 16761, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- linear OA(761, 16807, F7, 15) (dual of [16807, 16746, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 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(74, 19, F7, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,7)), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- 1 times truncation [i] based on linear OA(765, 16826, F7, 15) (dual of [16826, 16761, 16]-code), using
(50, 64, large)-Net in Base 7 — Upper bound on s
There is no (50, 64, large)-net in base 7, because
- 12 times m-reduction [i] would yield (50, 52, large)-net in base 7, but