Best Known (71, 101, s)-Nets in Base 7
(71, 101, 344)-Net over F7 — Constructive and digital
Digital (71, 101, 344)-net over F7, using
- base reduction for projective spaces (embedding PG(50,49) in PG(100,7)) for nets [i] based on digital (21, 51, 344)-net over F49, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
(71, 101, 1946)-Net over F7 — Digital
Digital (71, 101, 1946)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(7101, 1946, F7, 30) (dual of [1946, 1845, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(7101, 2401, F7, 30) (dual of [2401, 2300, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(7101, 2401, F7, 30) (dual of [2401, 2300, 31]-code), using
(71, 101, 524728)-Net in Base 7 — Upper bound on s
There is no (71, 101, 524729)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 22 641911 390228 651346 705719 977654 297168 154938 362397 970401 424107 933939 862984 307050 634103 > 7101 [i]