Best Known (98−22, 98, s)-Nets in Base 16
(98−22, 98, 11940)-Net over F16 — Constructive and digital
Digital (76, 98, 11940)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 24)-net over F16, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- net from sequence [i] based on digital (1, 23)-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 (1, 12, 24)-net over F16, using
(98−22, 98, 23831)-Net in Base 16 — Constructive
(76, 98, 23831)-net in base 16, using
- 162 times duplication [i] based on (74, 96, 23831)-net in base 16, using
- base change [i] based on digital (42, 64, 23831)-net over F64, using
- net defined by OOA [i] based on linear OOA(6464, 23831, F64, 22, 22) (dual of [(23831, 22), 524218, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(6464, 262141, F64, 22) (dual of [262141, 262077, 23]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(6464, 262144, F64, 22) (dual of [262144, 262080, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(6464, 262141, F64, 22) (dual of [262141, 262077, 23]-code), using
- net defined by OOA [i] based on linear OOA(6464, 23831, F64, 22, 22) (dual of [(23831, 22), 524218, 23]-NRT-code), using
- base change [i] based on digital (42, 64, 23831)-net over F64, using
(98−22, 98, 240795)-Net over F16 — Digital
Digital (76, 98, 240795)-net over F16, using
(98−22, 98, large)-Net in Base 16 — Upper bound on s
There is no (76, 98, large)-net in base 16, because
- 20 times m-reduction [i] would yield (76, 78, large)-net in base 16, but