Best Known (131−30, 131, s)-Nets in Base 8
(131−30, 131, 2184)-Net over F8 — Constructive and digital
Digital (101, 131, 2184)-net over F8, using
- net defined by OOA [i] based on linear OOA(8131, 2184, F8, 30, 30) (dual of [(2184, 30), 65389, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(8131, 32760, F8, 30) (dual of [32760, 32629, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(8131, 32768, F8, 30) (dual of [32768, 32637, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(8131, 32768, F8, 30) (dual of [32768, 32637, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(8131, 32760, F8, 30) (dual of [32760, 32629, 31]-code), using
(131−30, 131, 25150)-Net over F8 — Digital
Digital (101, 131, 25150)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8131, 25150, F8, 30) (dual of [25150, 25019, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(8131, 32768, F8, 30) (dual of [32768, 32637, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(8131, 32768, F8, 30) (dual of [32768, 32637, 31]-code), using
(131−30, 131, large)-Net in Base 8 — Upper bound on s
There is no (101, 131, large)-net in base 8, because
- 28 times m-reduction [i] would yield (101, 103, large)-net in base 8, but