Best Known (63−53, 63, s)-Nets in Base 128
(63−53, 63, 288)-Net over F128 — Constructive and digital
Digital (10, 63, 288)-net over F128, using
- t-expansion [i] based on digital (9, 63, 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
(63−53, 63, 296)-Net over F128 — Digital
Digital (10, 63, 296)-net over F128, using
- net from sequence [i] based on digital (10, 295)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 10 and N(F) ≥ 296, using
(63−53, 63, 321)-Net in Base 128
(10, 63, 321)-net in base 128, using
- 1 times m-reduction [i] based on (10, 64, 321)-net in base 128, using
- base change [i] based on digital (2, 56, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 56, 321)-net over F256, using
(63−53, 63, 8785)-Net in Base 128 — Upper bound on s
There is no (10, 63, 8786)-net in base 128, because
- 1 times m-reduction [i] would yield (10, 62, 8786)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 44479 568973 080907 266908 266384 369988 474396 357413 982504 371345 618065 647591 417683 745581 798195 624423 008908 831102 057007 360918 418563 511520 > 12862 [i]