Best Known (120−22, 120, s)-Nets in Base 16
(120−22, 120, 95391)-Net over F16 — Constructive and digital
Digital (98, 120, 95391)-net over F16, using
- 161 times duplication [i] based on digital (97, 119, 95391)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 17, 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 (80, 102, 95326)-net over F16, using
- net defined by OOA [i] based on linear OOA(16102, 95326, F16, 22, 22) (dual of [(95326, 22), 2097070, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(16102, 1048586, F16, 22) (dual of [1048586, 1048484, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(16102, 1048587, F16, 22) (dual of [1048587, 1048485, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(16101, 1048576, F16, 22) (dual of [1048576, 1048475, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(161, 11, F16, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(16102, 1048587, F16, 22) (dual of [1048587, 1048485, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(16102, 1048586, F16, 22) (dual of [1048586, 1048484, 23]-code), using
- net defined by OOA [i] based on linear OOA(16102, 95326, F16, 22, 22) (dual of [(95326, 22), 2097070, 23]-NRT-code), using
- digital (6, 17, 65)-net over F16, using
- (u, u+v)-construction [i] based on
(120−22, 120, 190652)-Net in Base 16 — Constructive
(98, 120, 190652)-net in base 16, using
- net defined by OOA [i] based on OOA(16120, 190652, S16, 22, 22), using
- OA 11-folding and stacking [i] based on OA(16120, 2097172, S16, 22), using
- 1 times code embedding in larger space [i] based on OA(16119, 2097171, S16, 22), using
- discarding parts of the base [i] based on linear OA(12868, 2097171, F128, 22) (dual of [2097171, 2097103, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12849, 2097152, F128, 17) (dual of [2097152, 2097103, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(21) ⊂ Ce(16) [i] based on
- discarding parts of the base [i] based on linear OA(12868, 2097171, F128, 22) (dual of [2097171, 2097103, 23]-code), using
- 1 times code embedding in larger space [i] based on OA(16119, 2097171, S16, 22), using
- OA 11-folding and stacking [i] based on OA(16120, 2097172, S16, 22), using
(120−22, 120, 4396306)-Net over F16 — Digital
Digital (98, 120, 4396306)-net over F16, using
(120−22, 120, large)-Net in Base 16 — Upper bound on s
There is no (98, 120, large)-net in base 16, because
- 20 times m-reduction [i] would yield (98, 100, large)-net in base 16, but