MinT - Best Known (8, 8+43, s)-Nets in Base 256

Best Known (8, 8+43, s)-Nets in Base 256

(8, 8+43, 265)-Net over F₂₅₆ — Constructive and digital

Digital (8, 51, 265)-net over F₂₅₆, using

net from sequence [i] based on digital (8, 264)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(8, 8+43, 513)-Net over F₂₅₆ — Digital

Digital (8, 51, 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]

(8, 8+43, 18434)-Net in Base 256 — Upper bound on s

There is no (8, 51, 18435)-net in base 256, because

1 times m-reduction [i] would yield (8, 50, 18435)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 2 585186 826961 581283 817632 862897 254277 337362 981054 231125 031439 832793 931953 925417 889878 705981 058728 112713 038127 898833 458176 > 256⁵⁰ [i]