Best Known (118, 141, s)-Nets in Base 8
(118, 141, 190650)-Net over F8 — Constructive and digital
Digital (118, 141, 190650)-net over F8, using
- net defined by OOA [i] based on linear OOA(8141, 190650, F8, 23, 23) (dual of [(190650, 23), 4384809, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8141, 2097151, F8, 23) (dual of [2097151, 2097010, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(8141, 2097152, F8, 23) (dual of [2097152, 2097011, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(8141, 2097152, F8, 23) (dual of [2097152, 2097011, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8141, 2097151, F8, 23) (dual of [2097151, 2097010, 24]-code), using
(118, 141, 1300140)-Net over F8 — Digital
Digital (118, 141, 1300140)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8141, 1300140, F8, 23) (dual of [1300140, 1299999, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(8141, 2097152, F8, 23) (dual of [2097152, 2097011, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(8141, 2097152, F8, 23) (dual of [2097152, 2097011, 24]-code), using
(118, 141, large)-Net in Base 8 — Upper bound on s
There is no (118, 141, large)-net in base 8, because
- 21 times m-reduction [i] would yield (118, 120, large)-net in base 8, but