Best Known (43, 43+12, s)-Nets in Base 16
(43, 43+12, 21884)-Net over F16 — Constructive and digital
Digital (43, 55, 21884)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (3, 9, 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 (34, 46, 21846)-net over F16, using
- net defined by OOA [i] based on linear OOA(1646, 21846, F16, 12, 12) (dual of [(21846, 12), 262106, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(1646, 131076, F16, 12) (dual of [131076, 131030, 13]-code), using
- trace code [i] based on linear OA(25623, 65538, F256, 12) (dual of [65538, 65515, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(25621, 65536, F256, 11) (dual of [65536, 65515, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(11) ⊂ Ce(10) [i] based on
- trace code [i] based on linear OA(25623, 65538, F256, 12) (dual of [65538, 65515, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(1646, 131076, F16, 12) (dual of [131076, 131030, 13]-code), using
- net defined by OOA [i] based on linear OOA(1646, 21846, F16, 12, 12) (dual of [(21846, 12), 262106, 13]-NRT-code), using
- digital (3, 9, 38)-net over F16, using
(43, 43+12, 43692)-Net in Base 16 — Constructive
(43, 55, 43692)-net in base 16, using
- 161 times duplication [i] based on (42, 54, 43692)-net in base 16, using
- base change [i] based on digital (24, 36, 43692)-net over F64, using
- net defined by OOA [i] based on linear OOA(6436, 43692, F64, 12, 12) (dual of [(43692, 12), 524268, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(6436, 262152, F64, 12) (dual of [262152, 262116, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(6436, 262155, F64, 12) (dual of [262155, 262119, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(6434, 262144, F64, 12) (dual of [262144, 262110, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(6425, 262144, F64, 9) (dual of [262144, 262119, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(11) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(6436, 262155, F64, 12) (dual of [262155, 262119, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(6436, 262152, F64, 12) (dual of [262152, 262116, 13]-code), using
- net defined by OOA [i] based on linear OOA(6436, 43692, F64, 12, 12) (dual of [(43692, 12), 524268, 13]-NRT-code), using
- base change [i] based on digital (24, 36, 43692)-net over F64, using
(43, 43+12, 343186)-Net over F16 — Digital
Digital (43, 55, 343186)-net over F16, using
(43, 43+12, large)-Net in Base 16 — Upper bound on s
There is no (43, 55, large)-net in base 16, because
- 10 times m-reduction [i] would yield (43, 45, large)-net in base 16, but