Best Known (100−22, 100, s)-Nets in Base 16
(100−22, 100, 11954)-Net over F16 — Constructive and digital
Digital (78, 100, 11954)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (3, 14, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- digital (64, 86, 11916)-net over F16, using
- net defined by OOA [i] based on linear OOA(1686, 11916, F16, 22, 22) (dual of [(11916, 22), 262066, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(1686, 131076, F16, 22) (dual of [131076, 130990, 23]-code), using
- trace code [i] based on linear OA(25643, 65538, F256, 22) (dual of [65538, 65495, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- trace code [i] based on linear OA(25643, 65538, F256, 22) (dual of [65538, 65495, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(1686, 131076, F16, 22) (dual of [131076, 130990, 23]-code), using
- net defined by OOA [i] based on linear OOA(1686, 11916, F16, 22, 22) (dual of [(11916, 22), 262066, 23]-NRT-code), using
- digital (3, 14, 38)-net over F16, using
(100−22, 100, 23832)-Net in Base 16 — Constructive
(78, 100, 23832)-net in base 16, using
- 161 times duplication [i] based on (77, 99, 23832)-net in base 16, using
- base change [i] based on digital (44, 66, 23832)-net over F64, using
- net defined by OOA [i] based on linear OOA(6466, 23832, F64, 22, 22) (dual of [(23832, 22), 524238, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(6466, 262152, F64, 22) (dual of [262152, 262086, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(6466, 262155, F64, 22) (dual of [262155, 262089, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(6464, 262144, F64, 22) (dual of [262144, 262080, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(6455, 262144, F64, 19) (dual of [262144, 262089, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(642, 11, F64, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(6466, 262155, F64, 22) (dual of [262155, 262089, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(6466, 262152, F64, 22) (dual of [262152, 262086, 23]-code), using
- net defined by OOA [i] based on linear OOA(6466, 23832, F64, 22, 22) (dual of [(23832, 22), 524238, 23]-NRT-code), using
- base change [i] based on digital (44, 66, 23832)-net over F64, using
(100−22, 100, 313560)-Net over F16 — Digital
Digital (78, 100, 313560)-net over F16, using
(100−22, 100, large)-Net in Base 16 — Upper bound on s
There is no (78, 100, large)-net in base 16, because
- 20 times m-reduction [i] would yield (78, 80, large)-net in base 16, but