MinT - Best Known (63−42, 63, s)-Nets in Base 256

Best Known (63−42, 63, s)-Nets in Base 256

(63−42, 63, 514)-Net over F₂₅₆ — Constructive and digital

Digital (21, 63, 514)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (0, 21, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]
2. digital (0, 42, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(63−42, 63, 571037)-Net in Base 256 — Upper bound on s

There is no (21, 63, 571038)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 52 375249 355524 872475 008646 118035 060621 985328 111046 536525 221477 780038 514963 050972 805630 186990 121519 238233 562358 628942 681131 388235 448692 159605 089492 379991 > 256⁶³ [i]