Best Known (35−11, 35, s)-Nets in Base 49
(35−11, 35, 23533)-Net over F49 — Constructive and digital
Digital (24, 35, 23533)-net over F49, using
- net defined by OOA [i] based on linear OOA(4935, 23533, F49, 11, 11) (dual of [(23533, 11), 258828, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(4935, 117666, F49, 11) (dual of [117666, 117631, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(4935, 117668, F49, 11) (dual of [117668, 117633, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(5) [i] based on
- linear OA(4931, 117649, F49, 11) (dual of [117649, 117618, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(4916, 117649, F49, 6) (dual of [117649, 117633, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(494, 19, F49, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,49)), using
- discarding factors / shortening the dual code based on linear OA(494, 49, F49, 4) (dual of [49, 45, 5]-code or 49-arc in PG(3,49)), using
- Reed–Solomon code RS(45,49) [i]
- discarding factors / shortening the dual code based on linear OA(494, 49, F49, 4) (dual of [49, 45, 5]-code or 49-arc in PG(3,49)), using
- construction X applied to Ce(10) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(4935, 117668, F49, 11) (dual of [117668, 117633, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(4935, 117666, F49, 11) (dual of [117666, 117631, 12]-code), using
(35−11, 35, 117668)-Net over F49 — Digital
Digital (24, 35, 117668)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4935, 117668, F49, 11) (dual of [117668, 117633, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(5) [i] based on
- linear OA(4931, 117649, F49, 11) (dual of [117649, 117618, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(4916, 117649, F49, 6) (dual of [117649, 117633, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(494, 19, F49, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,49)), using
- discarding factors / shortening the dual code based on linear OA(494, 49, F49, 4) (dual of [49, 45, 5]-code or 49-arc in PG(3,49)), using
- Reed–Solomon code RS(45,49) [i]
- discarding factors / shortening the dual code based on linear OA(494, 49, F49, 4) (dual of [49, 45, 5]-code or 49-arc in PG(3,49)), using
- construction X applied to Ce(10) ⊂ Ce(5) [i] based on
(35−11, 35, large)-Net in Base 49 — Upper bound on s
There is no (24, 35, large)-net in base 49, because
- 9 times m-reduction [i] would yield (24, 26, large)-net in base 49, but