Best Known (81, 98, s)-Nets in Base 5
(81, 98, 9769)-Net over F5 — Constructive and digital
Digital (81, 98, 9769)-net over F5, using
- net defined by OOA [i] based on linear OOA(598, 9769, F5, 17, 17) (dual of [(9769, 17), 165975, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(598, 78153, F5, 17) (dual of [78153, 78055, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(598, 78155, F5, 17) (dual of [78155, 78057, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- linear OA(592, 78125, F5, 17) (dual of [78125, 78033, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(564, 78125, F5, 12) (dual of [78125, 78061, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(598, 78155, F5, 17) (dual of [78155, 78057, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(598, 78153, F5, 17) (dual of [78153, 78055, 18]-code), using
(81, 98, 53165)-Net over F5 — Digital
Digital (81, 98, 53165)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(598, 53165, F5, 17) (dual of [53165, 53067, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(598, 78155, F5, 17) (dual of [78155, 78057, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- linear OA(592, 78125, F5, 17) (dual of [78125, 78033, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(564, 78125, F5, 12) (dual of [78125, 78061, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(598, 78155, F5, 17) (dual of [78155, 78057, 18]-code), using
(81, 98, large)-Net in Base 5 — Upper bound on s
There is no (81, 98, large)-net in base 5, because
- 15 times m-reduction [i] would yield (81, 83, large)-net in base 5, but