Best Known (70, 95, s)-Nets in Base 4
(70, 95, 384)-Net over F4 — Constructive and digital
Digital (70, 95, 384)-net over F4, using
- t-expansion [i] based on digital (69, 95, 384)-net over F4, using
- 1 times m-reduction [i] based on digital (69, 96, 384)-net over F4, using
- trace code for nets [i] based on digital (5, 32, 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, 32, 128)-net over F64, using
- 1 times m-reduction [i] based on digital (69, 96, 384)-net over F4, using
(70, 95, 450)-Net in Base 4 — Constructive
(70, 95, 450)-net in base 4, using
- 1 times m-reduction [i] based on (70, 96, 450)-net in base 4, using
- trace code for nets [i] based on (6, 32, 150)-net in base 64, using
- 3 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
- 3 times m-reduction [i] based on (6, 35, 150)-net in base 64, using
- trace code for nets [i] based on (6, 32, 150)-net in base 64, using
(70, 95, 890)-Net over F4 — Digital
Digital (70, 95, 890)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(495, 890, F4, 25) (dual of [890, 795, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(495, 1023, F4, 25) (dual of [1023, 928, 26]-code), using
- 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]
- discarding factors / shortening the dual code based on linear OA(495, 1023, F4, 25) (dual of [1023, 928, 26]-code), using
(70, 95, 91692)-Net in Base 4 — Upper bound on s
There is no (70, 95, 91693)-net in base 4, because
- 1 times m-reduction [i] would yield (70, 94, 91693)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 392 366732 508157 664394 041616 142467 766176 421911 015009 753445 > 494 [i]