Best Known (91, 108, s)-Nets in Base 4
(91, 108, 8206)-Net over F4 — Constructive and digital
Digital (91, 108, 8206)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (3, 11, 14)-net over F4, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- digital (80, 97, 8192)-net over F4, using
- net defined by OOA [i] based on linear OOA(497, 8192, F4, 17, 17) (dual of [(8192, 17), 139167, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(497, 65537, F4, 17) (dual of [65537, 65440, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(497, 65537, F4, 17) (dual of [65537, 65440, 18]-code), using
- net defined by OOA [i] based on linear OOA(497, 8192, F4, 17, 17) (dual of [(8192, 17), 139167, 18]-NRT-code), using
- digital (3, 11, 14)-net over F4, using
(91, 108, 42191)-Net over F4 — Digital
Digital (91, 108, 42191)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4108, 42191, F4, 17) (dual of [42191, 42083, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4108, 65580, F4, 17) (dual of [65580, 65472, 18]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4107, 65579, F4, 17) (dual of [65579, 65472, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- linear OA(497, 65537, F4, 17) (dual of [65537, 65440, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(465, 65537, F4, 11) (dual of [65537, 65472, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(410, 42, F4, 5) (dual of [42, 32, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4107, 65579, F4, 17) (dual of [65579, 65472, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4108, 65580, F4, 17) (dual of [65580, 65472, 18]-code), using
(91, 108, large)-Net in Base 4 — Upper bound on s
There is no (91, 108, large)-net in base 4, because
- 15 times m-reduction [i] would yield (91, 93, large)-net in base 4, but