Best Known (46−11, 46, s)-Nets in Base 7
(46−11, 46, 3362)-Net over F7 — Constructive and digital
Digital (35, 46, 3362)-net over F7, using
- net defined by OOA [i] based on linear OOA(746, 3362, F7, 11, 11) (dual of [(3362, 11), 36936, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(746, 16811, F7, 11) (dual of [16811, 16765, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(746, 16812, F7, 11) (dual of [16812, 16766, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [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(741, 16807, F7, 10) (dual of [16807, 16766, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(70, 5, F7, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(746, 16812, F7, 11) (dual of [16812, 16766, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(746, 16811, F7, 11) (dual of [16811, 16765, 12]-code), using
(46−11, 46, 11612)-Net over F7 — Digital
Digital (35, 46, 11612)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(746, 11612, F7, 11) (dual of [11612, 11566, 12]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(746, 16807, F7, 11) (dual of [16807, 16761, 12]-code), using
(46−11, 46, large)-Net in Base 7 — Upper bound on s
There is no (35, 46, large)-net in base 7, because
- 9 times m-reduction [i] would yield (35, 37, large)-net in base 7, but