Best Known (23, 53, s)-Nets in Base 81
(23, 53, 370)-Net over F81 — Constructive and digital
Digital (23, 53, 370)-net over F81, using
- t-expansion [i] based on digital (16, 53, 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
(23, 53, 465)-Net over F81 — Digital
Digital (23, 53, 465)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8153, 465, F81, 30) (dual of [465, 412, 31]-code), using
- 88 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 8 times 0, 1, 25 times 0, 1, 49 times 0) [i] based on linear OA(8146, 370, F81, 30) (dual of [370, 324, 31]-code), using
- extended algebraic-geometric code AGe(F,339P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- 88 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 8 times 0, 1, 25 times 0, 1, 49 times 0) [i] based on linear OA(8146, 370, F81, 30) (dual of [370, 324, 31]-code), using
(23, 53, 444614)-Net in Base 81 — Upper bound on s
There is no (23, 53, 444615)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 141161 790678 656381 507909 315039 878759 966378 954691 388014 188573 155783 923421 748160 529166 852822 929295 778001 > 8153 [i]