Best Known (22, 30, s)-Nets in Base 32
(22, 30, 262146)-Net over F32 — Constructive and digital
Digital (22, 30, 262146)-net over F32, using
- net defined by OOA [i] based on linear OOA(3230, 262146, F32, 8, 8) (dual of [(262146, 8), 2097138, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3230, 1048584, F32, 8) (dual of [1048584, 1048554, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(3230, 1048585, F32, 8) (dual of [1048585, 1048555, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(3229, 1048576, F32, 8) (dual of [1048576, 1048547, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(3221, 1048576, F32, 6) (dual of [1048576, 1048555, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(321, 9, F32, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(3230, 1048585, F32, 8) (dual of [1048585, 1048555, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(3230, 1048584, F32, 8) (dual of [1048584, 1048554, 9]-code), using
(22, 30, 1048586)-Net over F32 — Digital
Digital (22, 30, 1048586)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3230, 1048586, F32, 8) (dual of [1048586, 1048556, 9]-code), using
- construction X4 applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(3229, 1048576, F32, 8) (dual of [1048576, 1048547, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(3221, 1048576, F32, 6) (dual of [1048576, 1048555, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(329, 10, F32, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,32)), using
- dual of repetition code with length 10 [i]
- linear OA(321, 10, F32, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- Reed–Solomon code RS(31,32) [i]
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- construction X4 applied to Ce(7) ⊂ Ce(5) [i] based on
(22, 30, large)-Net in Base 32 — Upper bound on s
There is no (22, 30, large)-net in base 32, because
- 6 times m-reduction [i] would yield (22, 24, large)-net in base 32, but