MinT - Best Known (160, 160+53, s)-Nets in Base 4

Best Known (160, 160+53, s)-Nets in Base 4

(160, 160+53, 1028)-Net over F₄ — Constructive and digital

Digital (160, 213, 1028)-net over F₄, using

4¹ times duplication [i] based on digital (159, 212, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 53, 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]

(160, 160+53, 1998)-Net over F₄ — Digital

Digital (160, 213, 1998)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(160, 160+53, 285262)-Net in Base 4 — Upper bound on s

There is no (160, 213, 285263)-net in base 4, because

1 times m-reduction [i] would yield (160, 212, 285263)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 43 326435 728319 061217 590121 224379 924085 251756 850404 645071 509525 702597 516250 356347 738014 258663 451058 859613 686356 491067 757671 628660 > 4²¹² [i]