Best Known (23, 35, s)-Nets in Base 49
(23, 35, 19609)-Net over F49 — Constructive and digital
Digital (23, 35, 19609)-net over F49, using
- net defined by OOA [i] based on linear OOA(4935, 19609, F49, 12, 12) (dual of [(19609, 12), 235273, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(4935, 117654, F49, 12) (dual of [117654, 117619, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(4935, 117656, F49, 12) (dual of [117656, 117621, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(4934, 117649, F49, 12) (dual of [117649, 117615, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4928, 117649, F49, 10) (dual of [117649, 117621, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(491, 7, F49, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(4935, 117656, F49, 12) (dual of [117656, 117621, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(4935, 117654, F49, 12) (dual of [117654, 117619, 13]-code), using
(23, 35, 58828)-Net over F49 — Digital
Digital (23, 35, 58828)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4935, 58828, F49, 2, 12) (dual of [(58828, 2), 117621, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4935, 117656, F49, 12) (dual of [117656, 117621, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(4934, 117649, F49, 12) (dual of [117649, 117615, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4928, 117649, F49, 10) (dual of [117649, 117621, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(491, 7, F49, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- OOA 2-folding [i] based on linear OA(4935, 117656, F49, 12) (dual of [117656, 117621, 13]-code), using
(23, 35, large)-Net in Base 49 — Upper bound on s
There is no (23, 35, large)-net in base 49, because
- 10 times m-reduction [i] would yield (23, 25, large)-net in base 49, but