Best Known (94, 126, s)-Nets in Base 4
(94, 126, 531)-Net over F4 — Constructive and digital
Digital (94, 126, 531)-net over F4, using
- t-expansion [i] based on digital (93, 126, 531)-net over F4, using
- 3 times m-reduction [i] based on digital (93, 129, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 43, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 43, 177)-net over F64, using
- 3 times m-reduction [i] based on digital (93, 129, 531)-net over F4, using
(94, 126, 576)-Net in Base 4 — Constructive
(94, 126, 576)-net in base 4, using
- t-expansion [i] based on (93, 126, 576)-net in base 4, using
- trace code for nets [i] based on (9, 42, 192)-net in base 64, using
- base change [i] based on digital (3, 36, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 36, 192)-net over F128, using
- trace code for nets [i] based on (9, 42, 192)-net in base 64, using
(94, 126, 1175)-Net over F4 — Digital
Digital (94, 126, 1175)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4126, 1175, F4, 32) (dual of [1175, 1049, 33]-code), using
- 137 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0, 1, 13 times 0, 1, 28 times 0, 1, 41 times 0, 1, 47 times 0) [i] based on linear OA(4121, 1033, F4, 32) (dual of [1033, 912, 33]-code), using
- construction XX applied to C1 = C([1022,29]), C2 = C([0,30]), C3 = C1 + C2 = C([0,29]), and C∩ = C1 ∩ C2 = C([1022,30]) [i] based on
- linear OA(4116, 1023, F4, 31) (dual of [1023, 907, 32]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,29}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(4116, 1023, F4, 31) (dual of [1023, 907, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(4121, 1023, F4, 32) (dual of [1023, 902, 33]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,30}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4111, 1023, F4, 30) (dual of [1023, 912, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(40, 5, F4, 0) (dual of [5, 5, 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(40, 5, F4, 0) (dual of [5, 5, 1]-code) (see above)
- construction XX applied to C1 = C([1022,29]), C2 = C([0,30]), C3 = C1 + C2 = C([0,29]), and C∩ = C1 ∩ C2 = C([1022,30]) [i] based on
- 137 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0, 1, 13 times 0, 1, 28 times 0, 1, 41 times 0, 1, 47 times 0) [i] based on linear OA(4121, 1033, F4, 32) (dual of [1033, 912, 33]-code), using
(94, 126, 124909)-Net in Base 4 — Upper bound on s
There is no (94, 126, 124910)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 7237 518142 585797 707758 414383 287470 261647 961930 054771 082243 375359 066970 849878 > 4126 [i]