Best Known (102, 102+36, s)-Nets in Base 4
(102, 102+36, 531)-Net over F4 — Constructive and digital
Digital (102, 138, 531)-net over F4, using
- t-expansion [i] based on digital (101, 138, 531)-net over F4, using
- 3 times m-reduction [i] based on digital (101, 141, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 47, 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, 47, 177)-net over F64, using
- 3 times m-reduction [i] based on digital (101, 141, 531)-net over F4, using
(102, 102+36, 576)-Net in Base 4 — Constructive
(102, 138, 576)-net in base 4, using
- trace code for nets [i] based on (10, 46, 192)-net in base 64, using
- 3 times m-reduction [i] based on (10, 49, 192)-net in base 64, using
- base change [i] based on digital (3, 42, 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, 42, 192)-net over F128, using
- 3 times m-reduction [i] based on (10, 49, 192)-net in base 64, using
(102, 102+36, 1115)-Net over F4 — Digital
Digital (102, 138, 1115)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4138, 1115, F4, 36) (dual of [1115, 977, 37]-code), using
- 89 step Varšamov–Edel lengthening with (ri) = (1, 18 times 0, 1, 30 times 0, 1, 38 times 0) [i] based on linear OA(4135, 1023, F4, 36) (dual of [1023, 888, 37]-code), using
- the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- 89 step Varšamov–Edel lengthening with (ri) = (1, 18 times 0, 1, 30 times 0, 1, 38 times 0) [i] based on linear OA(4135, 1023, F4, 36) (dual of [1023, 888, 37]-code), using
(102, 102+36, 103930)-Net in Base 4 — Upper bound on s
There is no (102, 138, 103931)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 121435 026846 898536 602923 462082 481728 460295 854488 699972 014698 360764 560399 968554 414617 > 4138 [i]