Best Known (150−21, 150, s)-Nets in Base 5
(150−21, 150, 195315)-Net over F5 — Constructive and digital
Digital (129, 150, 195315)-net over F5, using
- 51 times duplication [i] based on digital (128, 149, 195315)-net over F5, using
- net defined by OOA [i] based on linear OOA(5149, 195315, F5, 21, 21) (dual of [(195315, 21), 4101466, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(5149, 1953151, F5, 21) (dual of [1953151, 1953002, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(5145, 1953125, F5, 21) (dual of [1953125, 1952980, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(5118, 1953125, F5, 17) (dual of [1953125, 1953007, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(54, 26, F5, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- OOA 10-folding and stacking with additional row [i] based on linear OA(5149, 1953151, F5, 21) (dual of [1953151, 1953002, 22]-code), using
- net defined by OOA [i] based on linear OOA(5149, 195315, F5, 21, 21) (dual of [(195315, 21), 4101466, 22]-NRT-code), using
(150−21, 150, 976578)-Net over F5 — Digital
Digital (129, 150, 976578)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5150, 976578, F5, 2, 21) (dual of [(976578, 2), 1953006, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5150, 1953156, F5, 21) (dual of [1953156, 1953006, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(5150, 1953157, F5, 21) (dual of [1953157, 1953007, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(5145, 1953125, F5, 21) (dual of [1953125, 1952980, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(5118, 1953125, F5, 17) (dual of [1953125, 1953007, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(55, 32, F5, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(5150, 1953157, F5, 21) (dual of [1953157, 1953007, 22]-code), using
- OOA 2-folding [i] based on linear OA(5150, 1953156, F5, 21) (dual of [1953156, 1953006, 22]-code), using
(150−21, 150, large)-Net in Base 5 — Upper bound on s
There is no (129, 150, large)-net in base 5, because
- 19 times m-reduction [i] would yield (129, 131, large)-net in base 5, but