Best Known (100, 100+16, s)-Nets in Base 5
(100, 100+16, 244146)-Net over F5 — Constructive and digital
Digital (100, 116, 244146)-net over F5, using
- net defined by OOA [i] based on linear OOA(5116, 244146, F5, 16, 16) (dual of [(244146, 16), 3906220, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(5116, 1953168, F5, 16) (dual of [1953168, 1953052, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(5109, 1953125, F5, 16) (dual of [1953125, 1953016, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(573, 1953125, F5, 11) (dual of [1953125, 1953052, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(57, 43, F5, 4) (dual of [43, 36, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 5]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- OA 8-folding and stacking [i] based on linear OA(5116, 1953168, F5, 16) (dual of [1953168, 1953052, 17]-code), using
(100, 100+16, 976584)-Net over F5 — Digital
Digital (100, 116, 976584)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5116, 976584, F5, 2, 16) (dual of [(976584, 2), 1953052, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5116, 1953168, F5, 16) (dual of [1953168, 1953052, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(5109, 1953125, F5, 16) (dual of [1953125, 1953016, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(573, 1953125, F5, 11) (dual of [1953125, 1953052, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(57, 43, F5, 4) (dual of [43, 36, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 5]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- OOA 2-folding [i] based on linear OA(5116, 1953168, F5, 16) (dual of [1953168, 1953052, 17]-code), using
(100, 100+16, large)-Net in Base 5 — Upper bound on s
There is no (100, 116, large)-net in base 5, because
- 14 times m-reduction [i] would yield (100, 102, large)-net in base 5, but