Best Known (79−19, 79, s)-Nets in Base 32
(79−19, 79, 116512)-Net over F32 — Constructive and digital
Digital (60, 79, 116512)-net over F32, using
- net defined by OOA [i] based on linear OOA(3279, 116512, F32, 19, 19) (dual of [(116512, 19), 2213649, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3279, 1048609, F32, 19) (dual of [1048609, 1048530, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(11) [i] based on
- linear OA(3273, 1048576, F32, 19) (dual of [1048576, 1048503, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3245, 1048576, F32, 12) (dual of [1048576, 1048531, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(326, 33, F32, 6) (dual of [33, 27, 7]-code or 33-arc in PG(5,32)), using
- extended Reed–Solomon code RSe(27,32) [i]
- construction X applied to Ce(18) ⊂ Ce(11) [i] based on
- OOA 9-folding and stacking with additional row [i] based on linear OA(3279, 1048609, F32, 19) (dual of [1048609, 1048530, 20]-code), using
(79−19, 79, 233017)-Net in Base 32 — Constructive
(60, 79, 233017)-net in base 32, using
- 322 times duplication [i] based on (58, 77, 233017)-net in base 32, using
- base change [i] based on digital (36, 55, 233017)-net over F128, using
- net defined by OOA [i] based on linear OOA(12855, 233017, F128, 19, 19) (dual of [(233017, 19), 4427268, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(12855, 2097154, F128, 19) (dual of [2097154, 2097099, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(12855, 2097155, F128, 19) (dual of [2097155, 2097100, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(12855, 2097152, F128, 19) (dual of [2097152, 2097097, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(12852, 2097152, F128, 18) (dual of [2097152, 2097100, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(12855, 2097155, F128, 19) (dual of [2097155, 2097100, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(12855, 2097154, F128, 19) (dual of [2097154, 2097099, 20]-code), using
- net defined by OOA [i] based on linear OOA(12855, 233017, F128, 19, 19) (dual of [(233017, 19), 4427268, 20]-NRT-code), using
- base change [i] based on digital (36, 55, 233017)-net over F128, using
(79−19, 79, 1048609)-Net over F32 — Digital
Digital (60, 79, 1048609)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3279, 1048609, F32, 19) (dual of [1048609, 1048530, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(11) [i] based on
- linear OA(3273, 1048576, F32, 19) (dual of [1048576, 1048503, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3245, 1048576, F32, 12) (dual of [1048576, 1048531, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(326, 33, F32, 6) (dual of [33, 27, 7]-code or 33-arc in PG(5,32)), using
- extended Reed–Solomon code RSe(27,32) [i]
- construction X applied to Ce(18) ⊂ Ce(11) [i] based on
(79−19, 79, large)-Net in Base 32 — Upper bound on s
There is no (60, 79, large)-net in base 32, because
- 17 times m-reduction [i] would yield (60, 62, large)-net in base 32, but