Best Known (28−21, 28, s)-Nets in Base 128
(28−21, 28, 216)-Net over F128 — Constructive and digital
Digital (7, 28, 216)-net over F128, using
- t-expansion [i] based on digital (5, 28, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
(28−21, 28, 260)-Net in Base 128 — Constructive
(7, 28, 260)-net in base 128, using
- 4 times m-reduction [i] based on (7, 32, 260)-net in base 128, using
- base change [i] based on digital (3, 28, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- base change [i] based on digital (3, 28, 260)-net over F256, using
(28−21, 28, 262)-Net over F128 — Digital
Digital (7, 28, 262)-net over F128, using
- net from sequence [i] based on digital (7, 261)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 7 and N(F) ≥ 262, using
(28−21, 28, 321)-Net in Base 128
(7, 28, 321)-net in base 128, using
- 12 times m-reduction [i] based on (7, 40, 321)-net in base 128, using
- base change [i] based on digital (2, 35, 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, 35, 321)-net over F256, using
(28−21, 28, 17439)-Net in Base 128 — Upper bound on s
There is no (7, 28, 17440)-net in base 128, because
- 1 times m-reduction [i] would yield (7, 27, 17440)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 785 016845 664161 518559 730032 147646 553786 419243 395386 612517 > 12827 [i]