Best Known (35, 46, s)-Nets in Base 9
(35, 46, 11810)-Net over F9 — Constructive and digital
Digital (35, 46, 11810)-net over F9, using
- net defined by OOA [i] based on linear OOA(946, 11810, F9, 11, 11) (dual of [(11810, 11), 129864, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(946, 59051, F9, 11) (dual of [59051, 59005, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(946, 59054, F9, 11) (dual of [59054, 59008, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(946, 59049, F9, 11) (dual of [59049, 59003, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(941, 59049, F9, 10) (dual of [59049, 59008, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(90, 5, F9, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 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(946, 59054, F9, 11) (dual of [59054, 59008, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(946, 59051, F9, 11) (dual of [59051, 59005, 12]-code), using
(35, 46, 30606)-Net over F9 — Digital
Digital (35, 46, 30606)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(946, 30606, F9, 11) (dual of [30606, 30560, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(946, 59049, F9, 11) (dual of [59049, 59003, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(946, 59049, F9, 11) (dual of [59049, 59003, 12]-code), using
(35, 46, large)-Net in Base 9 — Upper bound on s
There is no (35, 46, large)-net in base 9, because
- 9 times m-reduction [i] would yield (35, 37, large)-net in base 9, but