MinT - Best Known (9, 52, s)-Nets in Base 256

Best Known (9, 52, s)-Nets in Base 256

(9, 52, 266)-Net over F₂₅₆ — Constructive and digital

Digital (9, 52, 266)-net over F₂₅₆, using

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

(9, 52, 513)-Net over F₂₅₆ — Digital

Digital (9, 52, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 52, 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, 52, 24007)-Net in Base 256 — Upper bound on s

There is no (9, 52, 24008)-net in base 256, because

1 times m-reduction [i] would yield (9, 51, 24008)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 661 156841 222702 793904 714515 937911 046433 348203 221511 911423 764533 997050 236784 067174 488342 114009 039208 598640 597472 413373 798716 > 256⁵¹ [i]