Best Known (98, 98+28, s)-Nets in Base 16
(98, 98+28, 9395)-Net over F16 — Constructive and digital
Digital (98, 126, 9395)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (2, 16, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- digital (82, 110, 9362)-net over F16, using
- net defined by OOA [i] based on linear OOA(16110, 9362, F16, 28, 28) (dual of [(9362, 28), 262026, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(16110, 131068, F16, 28) (dual of [131068, 130958, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(16110, 131072, F16, 28) (dual of [131072, 130962, 29]-code), using
- trace code [i] based on linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- trace code [i] based on linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(16110, 131072, F16, 28) (dual of [131072, 130962, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(16110, 131068, F16, 28) (dual of [131068, 130958, 29]-code), using
- net defined by OOA [i] based on linear OOA(16110, 9362, F16, 28, 28) (dual of [(9362, 28), 262026, 29]-NRT-code), using
- digital (2, 16, 33)-net over F16, using
(98, 98+28, 18725)-Net in Base 16 — Constructive
(98, 126, 18725)-net in base 16, using
- base change [i] based on digital (56, 84, 18725)-net over F64, using
- 641 times duplication [i] based on digital (55, 83, 18725)-net over F64, using
- net defined by OOA [i] based on linear OOA(6483, 18725, F64, 28, 28) (dual of [(18725, 28), 524217, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(6483, 262150, F64, 28) (dual of [262150, 262067, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(6483, 262151, F64, 28) (dual of [262151, 262068, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(6482, 262144, F64, 28) (dual of [262144, 262062, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(6476, 262144, F64, 26) (dual of [262144, 262068, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(6483, 262151, F64, 28) (dual of [262151, 262068, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(6483, 262150, F64, 28) (dual of [262150, 262067, 29]-code), using
- net defined by OOA [i] based on linear OOA(6483, 18725, F64, 28, 28) (dual of [(18725, 28), 524217, 29]-NRT-code), using
- 641 times duplication [i] based on digital (55, 83, 18725)-net over F64, using
(98, 98+28, 303083)-Net over F16 — Digital
Digital (98, 126, 303083)-net over F16, using
(98, 98+28, large)-Net in Base 16 — Upper bound on s
There is no (98, 126, large)-net in base 16, because
- 26 times m-reduction [i] would yield (98, 100, large)-net in base 16, but