Best Known (30, 30+16, s)-Nets in Base 25
(30, 30+16, 1953)-Net over F25 — Constructive and digital
Digital (30, 46, 1953)-net over F25, using
- net defined by OOA [i] based on linear OOA(2546, 1953, F25, 16, 16) (dual of [(1953, 16), 31202, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2546, 15624, F25, 16) (dual of [15624, 15578, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2546, 15625, F25, 16) (dual of [15625, 15579, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2546, 15625, F25, 16) (dual of [15625, 15579, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2546, 15624, F25, 16) (dual of [15624, 15578, 17]-code), using
(30, 30+16, 7839)-Net over F25 — Digital
Digital (30, 46, 7839)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2546, 7839, F25, 16) (dual of [7839, 7793, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2546, 15625, F25, 16) (dual of [15625, 15579, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2546, 15625, F25, 16) (dual of [15625, 15579, 17]-code), using
(30, 30+16, large)-Net in Base 25 — Upper bound on s
There is no (30, 46, large)-net in base 25, because
- 14 times m-reduction [i] would yield (30, 32, large)-net in base 25, but