Best Known (73, 73+28, s)-Nets in Base 7
(73, 73+28, 688)-Net over F7 — Constructive and digital
Digital (73, 101, 688)-net over F7, using
- 3 times m-reduction [i] based on digital (73, 104, 688)-net over F7, using
- trace code for nets [i] based on digital (21, 52, 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
- trace code for nets [i] based on digital (21, 52, 344)-net over F49, using
(73, 73+28, 2669)-Net over F7 — Digital
Digital (73, 101, 2669)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(7101, 2669, F7, 28) (dual of [2669, 2568, 29]-code), using
- 263 step Varšamov–Edel lengthening with (ri) = (2, 5 times 0, 1, 29 times 0, 1, 83 times 0, 1, 142 times 0) [i] based on linear OA(796, 2401, F7, 28) (dual of [2401, 2305, 29]-code), using
- 1 times truncation [i] based on linear OA(797, 2402, F7, 29) (dual of [2402, 2305, 30]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2402 | 78−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(797, 2402, F7, 29) (dual of [2402, 2305, 30]-code), using
- 263 step Varšamov–Edel lengthening with (ri) = (2, 5 times 0, 1, 29 times 0, 1, 83 times 0, 1, 142 times 0) [i] based on linear OA(796, 2401, F7, 28) (dual of [2401, 2305, 29]-code), using
(73, 73+28, 1259163)-Net in Base 7 — Upper bound on s
There is no (73, 101, 1259164)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 22 641436 950734 214681 680177 575169 749854 733823 218645 451736 414327 680652 894978 583419 211081 > 7101 [i]