Best Known (16, 16+45, s)-Nets in Base 128
(16, 16+45, 288)-Net over F128 — Constructive and digital
Digital (16, 61, 288)-net over F128, using
- t-expansion [i] based on digital (9, 61, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
(16, 16+45, 386)-Net over F128 — Digital
Digital (16, 61, 386)-net over F128, using
- t-expansion [i] based on digital (15, 61, 386)-net over F128, using
- net from sequence [i] based on digital (15, 385)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 15 and N(F) ≥ 386, using
- net from sequence [i] based on digital (15, 385)-sequence over F128, using
(16, 16+45, 513)-Net in Base 128
(16, 61, 513)-net in base 128, using
- 3 times m-reduction [i] based on (16, 64, 513)-net in base 128, using
- base change [i] based on digital (8, 56, 513)-net over F256, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- base change [i] based on digital (8, 56, 513)-net over F256, using
(16, 16+45, 39798)-Net in Base 128 — Upper bound on s
There is no (16, 61, 39799)-net in base 128, because
- 1 times m-reduction [i] would yield (16, 60, 39799)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 2 708099 499431 995318 166041 612803 349574 580686 502474 606813 586055 316153 760533 773447 810296 706528 462210 837500 649767 341868 464496 635667 > 12860 [i]