Best Known (84, 102, s)-Nets in Base 5
(84, 102, 8682)-Net over F5 — Constructive and digital
Digital (84, 102, 8682)-net over F5, using
- 52 times duplication [i] based on digital (82, 100, 8682)-net over F5, using
- net defined by OOA [i] based on linear OOA(5100, 8682, F5, 18, 18) (dual of [(8682, 18), 156176, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(5100, 78138, F5, 18) (dual of [78138, 78038, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(5100, 78140, F5, 18) (dual of [78140, 78040, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- linear OA(599, 78125, F5, 18) (dual of [78125, 78026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(51, 15, F5, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(5100, 78140, F5, 18) (dual of [78140, 78040, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(5100, 78138, F5, 18) (dual of [78138, 78038, 19]-code), using
- net defined by OOA [i] based on linear OOA(5100, 8682, F5, 18, 18) (dual of [(8682, 18), 156176, 19]-NRT-code), using
(84, 102, 43916)-Net over F5 — Digital
Digital (84, 102, 43916)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5102, 43916, F5, 18) (dual of [43916, 43814, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(5102, 78143, F5, 18) (dual of [78143, 78041, 19]-code), using
- construction XX applied to Ce(17) ⊂ Ce(15) ⊂ Ce(13) [i] based on
- linear OA(599, 78125, F5, 18) (dual of [78125, 78026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(578, 78125, F5, 14) (dual of [78125, 78047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(51, 16, F5, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(51, 2, F5, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(17) ⊂ Ce(15) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(5102, 78143, F5, 18) (dual of [78143, 78041, 19]-code), using
(84, 102, large)-Net in Base 5 — Upper bound on s
There is no (84, 102, large)-net in base 5, because
- 16 times m-reduction [i] would yield (84, 86, large)-net in base 5, but