MinT - Best Known (9, 9+49, s)-Nets in Base 256

Best Known (9, 9+49, s)-Nets in Base 256

(9, 9+49, 266)-Net over F₂₅₆ — Constructive and digital

Digital (9, 58, 266)-net over F₂₅₆, using

net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(9, 9+49, 513)-Net over F₂₅₆ — Digital

Digital (9, 58, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 58, 513)-net over F₂₅₆, using
- net from sequence [i] based on digital (8, 512)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 8 and N(F) ≥ 513, using
    - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₂₅₆ [i]

(9, 9+49, 20143)-Net in Base 256 — Upper bound on s

There is no (9, 58, 20144)-net in base 256, because

1 times m-reduction [i] would yield (9, 57, 20144)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 186102 633233 453916 409265 342373 113184 040252 072930 041356 690891 807168 608938 509568 813874 779532 513463 770993 692244 476074 536424 898654 883074 810406 > 256⁵⁷ [i]