Best Known (98−26, 98, s)-Nets in Base 4
(98−26, 98, 384)-Net over F4 — Constructive and digital
Digital (72, 98, 384)-net over F4, using
- t-expansion [i] based on digital (71, 98, 384)-net over F4, using
- 1 times m-reduction [i] based on digital (71, 99, 384)-net over F4, using
- trace code for nets [i] based on digital (5, 33, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- trace code for nets [i] based on digital (5, 33, 128)-net over F64, using
- 1 times m-reduction [i] based on digital (71, 99, 384)-net over F4, using
(98−26, 98, 450)-Net in Base 4 — Constructive
(72, 98, 450)-net in base 4, using
- 1 times m-reduction [i] based on (72, 99, 450)-net in base 4, using
- trace code for nets [i] based on (6, 33, 150)-net in base 64, using
- 2 times m-reduction [i] based on (6, 35, 150)-net in base 64, using
- base change [i] based on digital (1, 30, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 30, 150)-net over F128, using
- 2 times m-reduction [i] based on (6, 35, 150)-net in base 64, using
- trace code for nets [i] based on (6, 33, 150)-net in base 64, using
(98−26, 98, 868)-Net over F4 — Digital
Digital (72, 98, 868)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(498, 868, F4, 26) (dual of [868, 770, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(498, 1032, F4, 26) (dual of [1032, 934, 27]-code), using
- construction XX applied to Ce(25) ⊂ Ce(24) ⊂ Ce(22) [i] based on
- linear OA(496, 1024, F4, 26) (dual of [1024, 928, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(491, 1024, F4, 25) (dual of [1024, 933, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(486, 1024, F4, 23) (dual of [1024, 938, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(40, 6, F4, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(25) ⊂ Ce(24) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(498, 1032, F4, 26) (dual of [1032, 934, 27]-code), using
(98−26, 98, 65286)-Net in Base 4 — Upper bound on s
There is no (72, 98, 65287)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 100446 944870 270498 916128 629060 059550 591389 630698 370942 681664 > 498 [i]