Best Known (91, 112, s)-Nets in Base 16
(91, 112, 104923)-Net over F16 — Constructive and digital
Digital (91, 112, 104923)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 16, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- digital (75, 96, 104858)-net over F16, using
- net defined by OOA [i] based on linear OOA(1696, 104858, F16, 21, 21) (dual of [(104858, 21), 2201922, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(1696, 1048581, F16, 21) (dual of [1048581, 1048485, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(1696, 1048576, F16, 21) (dual of [1048576, 1048480, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(1691, 1048576, F16, 20) (dual of [1048576, 1048485, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- OOA 10-folding and stacking with additional row [i] based on linear OA(1696, 1048581, F16, 21) (dual of [1048581, 1048485, 22]-code), using
- net defined by OOA [i] based on linear OOA(1696, 104858, F16, 21, 21) (dual of [(104858, 21), 2201922, 22]-NRT-code), using
- digital (6, 16, 65)-net over F16, using
(91, 112, 209716)-Net in Base 16 — Constructive
(91, 112, 209716)-net in base 16, using
- base change [i] based on digital (43, 64, 209716)-net over F128, using
- 1281 times duplication [i] based on digital (42, 63, 209716)-net over F128, using
- net defined by OOA [i] based on linear OOA(12863, 209716, F128, 21, 21) (dual of [(209716, 21), 4403973, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(12863, 2097161, F128, 21) (dual of [2097161, 2097098, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(12863, 2097163, F128, 21) (dual of [2097163, 2097100, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(17) [i] based on
- linear OA(12861, 2097152, F128, 21) (dual of [2097152, 2097091, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(12852, 2097152, F128, 18) (dual of [2097152, 2097100, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(20) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(12863, 2097163, F128, 21) (dual of [2097163, 2097100, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(12863, 2097161, F128, 21) (dual of [2097161, 2097098, 22]-code), using
- net defined by OOA [i] based on linear OOA(12863, 209716, F128, 21, 21) (dual of [(209716, 21), 4403973, 22]-NRT-code), using
- 1281 times duplication [i] based on digital (42, 63, 209716)-net over F128, using
(91, 112, 3063997)-Net over F16 — Digital
Digital (91, 112, 3063997)-net over F16, using
(91, 112, large)-Net in Base 16 — Upper bound on s
There is no (91, 112, large)-net in base 16, because
- 19 times m-reduction [i] would yield (91, 93, large)-net in base 16, but