Best Known (98, 98+16, s)-Nets in Base 4
(98, 98+16, 32772)-Net over F4 — Constructive and digital
Digital (98, 114, 32772)-net over F4, using
- net defined by OOA [i] based on linear OOA(4114, 32772, F4, 16, 16) (dual of [(32772, 16), 524238, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(4114, 262176, F4, 16) (dual of [262176, 262062, 17]-code), using
- strength reduction [i] based on linear OA(4114, 262176, F4, 17) (dual of [262176, 262062, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(4109, 262144, F4, 17) (dual of [262144, 262035, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(482, 262144, F4, 13) (dual of [262144, 262062, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(45, 32, F4, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- strength reduction [i] based on linear OA(4114, 262176, F4, 17) (dual of [262176, 262062, 18]-code), using
- OA 8-folding and stacking [i] based on linear OA(4114, 262176, F4, 16) (dual of [262176, 262062, 17]-code), using
(98, 98+16, 145811)-Net over F4 — Digital
Digital (98, 114, 145811)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4114, 145811, F4, 16) (dual of [145811, 145697, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4114, 262176, F4, 16) (dual of [262176, 262062, 17]-code), using
- strength reduction [i] based on linear OA(4114, 262176, F4, 17) (dual of [262176, 262062, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(4109, 262144, F4, 17) (dual of [262144, 262035, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(482, 262144, F4, 13) (dual of [262144, 262062, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(45, 32, F4, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- strength reduction [i] based on linear OA(4114, 262176, F4, 17) (dual of [262176, 262062, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4114, 262176, F4, 16) (dual of [262176, 262062, 17]-code), using
(98, 98+16, large)-Net in Base 4 — Upper bound on s
There is no (98, 114, large)-net in base 4, because
- 14 times m-reduction [i] would yield (98, 100, large)-net in base 4, but