Best Known (67, 93, s)-Nets in Base 9
(67, 93, 740)-Net over F9 — Constructive and digital
Digital (67, 93, 740)-net over F9, using
- 9 times m-reduction [i] based on digital (67, 102, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 51, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 51, 370)-net over F81, using
(67, 93, 5561)-Net over F9 — Digital
Digital (67, 93, 5561)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(993, 5561, F9, 26) (dual of [5561, 5468, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(993, 6561, F9, 26) (dual of [6561, 6468, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(993, 6561, F9, 26) (dual of [6561, 6468, 27]-code), using
(67, 93, 4751378)-Net in Base 9 — Upper bound on s
There is no (67, 93, 4751379)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 55533 409146 038537 161384 355020 800300 940491 735520 363572 988456 578411 000234 271433 020706 834617 > 993 [i]