Best Known (93, 93+21, s)-Nets in Base 16
(93, 93+21, 104924)-Net over F16 — Constructive and digital
Digital (93, 114, 104924)-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 (77, 98, 104859)-net over F16, using
- net defined by OOA [i] based on linear OOA(1698, 104859, F16, 21, 21) (dual of [(104859, 21), 2201941, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(1698, 1048591, F16, 21) (dual of [1048591, 1048493, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(1698, 1048593, F16, 21) (dual of [1048593, 1048495, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(17) [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(1681, 1048576, F16, 18) (dual of [1048576, 1048495, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(162, 17, F16, 2) (dual of [17, 15, 3]-code or 17-arc in PG(1,16)), using
- extended Reed–Solomon code RSe(15,16) [i]
- Hamming code H(2,16) [i]
- construction X applied to Ce(20) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(1698, 1048593, F16, 21) (dual of [1048593, 1048495, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(1698, 1048591, F16, 21) (dual of [1048591, 1048493, 22]-code), using
- net defined by OOA [i] based on linear OOA(1698, 104859, F16, 21, 21) (dual of [(104859, 21), 2201941, 22]-NRT-code), using
- digital (6, 16, 65)-net over F16, using
(93, 93+21, 209717)-Net in Base 16 — Constructive
(93, 114, 209717)-net in base 16, using
- net defined by OOA [i] based on OOA(16114, 209717, S16, 21, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(16114, 2097171, S16, 21), using
- discarding parts of the base [i] based on linear OA(12865, 2097171, F128, 21) (dual of [2097171, 2097106, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [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(12846, 2097152, F128, 16) (dual of [2097152, 2097106, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(1284, 19, F128, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,128)), using
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- Reed–Solomon code RS(124,128) [i]
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- discarding parts of the base [i] based on linear OA(12865, 2097171, F128, 21) (dual of [2097171, 2097106, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on OA(16114, 2097171, S16, 21), using
(93, 93+21, 4042965)-Net over F16 — Digital
Digital (93, 114, 4042965)-net over F16, using
(93, 93+21, large)-Net in Base 16 — Upper bound on s
There is no (93, 114, large)-net in base 16, because
- 19 times m-reduction [i] would yield (93, 95, large)-net in base 16, but