MinT - Best Known (16, 16+43, s)-Nets in Base 256

Best Known (16, 16+43, s)-Nets in Base 256

(16, 16+43, 273)-Net over F₂₅₆ — Constructive and digital

Digital (16, 59, 273)-net over F₂₅₆, using

net from sequence [i] based on digital (16, 272)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(16, 16+43, 513)-Net over F₂₅₆ — Digital

Digital (16, 59, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 59, 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]

(16, 16+43, 152494)-Net in Base 256 — Upper bound on s

There is no (16, 59, 152495)-net in base 256, because

1 times m-reduction [i] would yield (16, 58, 152495)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 47 639865 838303 832594 185625 712118 213799 384276 937152 424094 310671 300401 143529 953060 487183 815953 931993 846645 611750 422952 214061 099355 848266 144476 > 256⁵⁸ [i]